**Commenced**in January 2007

**Frequency:**Monthly

**Edition:**International

**Paper Count:**3738

# Search results for: positive solution.

##### 3738 Existence of Positive Solutions for Second-Order Difference Equation with Discrete Boundary Value Problem

**Authors:**
Thanin Sitthiwirattham,
Jiraporn Reunsumrit

**Abstract:**

We study the existence of positive solutions to the three points difference-summation boundary value problem. We show the existence of at least one positive solution if f is either superlinear or sublinear by applying the fixed point theorem due to Krasnoselskii in cones.

**Keywords:**
Positive solution,
Boundary value problem,
Fixed
point theorem,
Cone.

##### 3737 A New Inversion-free Method for Hermitian Positive Definite Solution of Matrix Equation

**Authors:**
Minghui Wang,
Juntao Zhang

**Abstract:**

An inversion-free iterative algorithm is presented for solving nonlinear matrix equation with a stepsize parameter t. The existence of the maximal solution is discussed in detail, and the method for finding it is proposed. Finally, two numerical examples are reported that show the efficiency of the method.

**Keywords:**
Inversion-free method,
Hermitian positive definite solution,
Maximal solution,
Convergence.

##### 3736 The Existence and Uniqueness of Positive Solution for Nonlinear Fractional Differential Equation Boundary Value Problem

**Authors:**
Chuanyun Gu,
Shouming Zhong

**Abstract:**

In this paper, the existence and uniqueness of positive solutions for nonlinear fractional differential equation boundary value problem is concerned by a fixed point theorem of a sum operator. Our results can not only guarantee the existence and uniqueness of positive solution, but also be applied to construct an iterative scheme for approximating it. Finally, the example is given to illustrate the main result.

**Keywords:**
Fractional differential equation,
Boundary value problem,
Positive solution,
Existence and uniqueness,
Fixed point theorem of a sum operator

##### 3735 A Numerical Algorithm for Positive Solutions of Concave and Convex Elliptic Equation on R2

**Authors:**
Hailong Zhu,
Zhaoxiang Li

**Abstract:**

In this paper we investigate numerically positive solutions of the equation -Δu = λuq+up with Dirichlet boundary condition in a boundary domain ╬® for λ > 0 and 0 < q < 1 < p < 2*, we will compute and visualize the range of λ, this problem achieves a numerical solution.

**Keywords:**
positive solutions,
concave-convex,
sub-super solution method,
pseudo arclength method.

##### 3734 Unique Positive Solution of Nonlinear Fractional Differential Equation Boundary Value Problem

**Authors:**
Fengxia Zheng

**Abstract:**

By using two new fixed point theorems for mixed monotone operators, the positive solution of nonlinear fractional differential equation boundary value problem is studied. Its existence and uniqueness is proved, and an iterative scheme is constructed to approximate it.

**Keywords:**
Fractional differential equation,
boundary value problem,
positive solution,
existence and uniqueness,
fixed point theorem,
mixed monotone operator.

##### 3733 A Novel Approach to Positive Almost Periodic Solution of BAM Neural Networks with Time-Varying Delays

**Abstract:**

In this paper, based on almost periodic functional hull theory and M-matrix theory, some sufficient conditions are established for the existence and uniqueness of positive almost periodic solution for a class of BAM neural networks with time-varying delays. An example is given to illustrate the main results.

**Keywords:**
Delayed BAM neural networks,
Hull theorem,
Mmatrix,
Almost periodic solution,
Global exponential stability.

##### 3732 On the Positive Definite Solutions of Nonlinear Matrix Equation

**Authors:**
Tian Baoguang,
Liang Chunyan,
Chen Nan

**Abstract:**

In this paper, the nonlinear matrix equation is investigated. Based on the fixed-point theory, the boundary and the existence of the solution with the case r>-δ_{i} are discussed. An algorithm that avoids matrix inversion with the case -1<-δ_{i}<0 is proposed.

**Keywords:**
Nonlinear matrix equation,
Positive definite solution,
The maximal-minimal solution,
Iterative method,
Free-inversion

##### 3731 A Sum Operator Method for Unique Positive Solution to a Class of Boundary Value Problem of Nonlinear Fractional Differential Equation

**Authors:**
Fengxia Zheng,
Chuanyun Gu

**Abstract:**

**Keywords:**
Fractional differential equation,
Boundary value
problem,
Positive solution,
Existence and uniqueness,
Fixed point
theorem of a sum operator.

##### 3730 Existence and Uniqueness of Positive Solution for Nonlinear Fractional Differential Equation with Integral Boundary Conditions

**Authors:**
Chuanyun Gu

**Abstract:**

**Keywords:**
Fractional differential equation,
positive solution,
existence and uniqueness,
fixed point theorem,
generalized concave
and convex operator,
integral boundary conditions.

##### 3729 The Positive Solution for Singular Eigenvalue Problem of One-dimensional p-Laplace Operator

**Authors:**
Lv Yuhua

**Abstract:**

In this paper, by constructing a special cone and using fixed point theorem and fixed point index theorem of cone, we get the existence of positive solution for a class of singular eigenvalue value problems with p-Laplace operator, which improved and generalized the result of related paper.

**Keywords:**
Cone,
fixed point index,
eigenvalue problem,
p-Laplace operator,
positive solutions.

##### 3728 Properties of a Stochastic Predator-Prey System with Holling II Functional Response

**Authors:**
Xianqing Liu,
Shouming Zhong,
Fuli Zhong,
Zijian Liu

**Abstract:**

In this paper, a stochastic predator-prey system with Holling II functional response is studied. First, we show that there is a unique positive solution to the system for any given positive initial value. Then, stochastically bounded of the positive solution to the stochastic system is derived. Moreover, sufficient conditions for global asymptotic stability are also established. In the end, some simulation figures are carried out to support the analytical findings.

**Keywords:**
stochastically bounded,
global stability,
Holling II
functional response,
white noise,
Markovian switching.

##### 3727 Positive Periodic Solutions for a Neutral Impulsive Delay Competition System

**Authors:**
Daiming Wang

**Abstract:**

In this paper, a neutral impulsive competition system with distributed delays is studied by using Mawhin-s coincidence degree theory and the mean value theorem of differential calculus. Sufficient conditions on the existence of positive periodic solution of the system are obtained.

**Keywords:**
Neutral impulsive delay system,
competitive system,
coincidence degree,
periodic solution,
existence.

##### 3726 Efficacy of Garlic and Chili Combination Solution on Cabbage Insect Pests and Crop Growth in Vietnam

**Authors:**
Nguyen Minh Tuan,
Bui Lan Anh,
Bui Nu Hoang Anh

**Abstract:**

The study was conducted to evaluate the efficiency of Garlic and Chili combination solution on control of insect pests in cabbage crop. The solution was sprayed at different intervals after transplanting. The efficiency of Garlic and chili combination solution on cabbage insect pests was measured. Results revealed that Garlic and chili combination solution was the effectively reduced cabbage insect pests. On other hand, the spray solution not only reduced the number of days required for the cabbage growth but also greatly enhanced the leaf number, head diameter, head weight, and quality of cabbage. Garlic and chili combination solution have positive effects on pests reduction and improve growth, yield and quality of cabbage vegetable.

**Keywords:**
Cabbage,
Garlic,
Chili,
Diamondback moth,
Cutworm,
Flea Beetle,
Quality.

##### 3725 Positive Almost Periodic Solutions for Neural Multi-Delay Logarithmic Population Model

**Authors:**
Zhouhong Li

**Abstract:**

In this paper, by applying Mawhin-s continuation theorem of coincidence degree theory, we study the existence of almost periodic solutions for neural multi-delay logarithmic population model and obtain one sufficient condition for the existence of positive almost periodic solution for the above equation. An example is employed to illustrate our result.

**Keywords:**
Almost periodic solution,
Multi-delay,
Logarithmic population model,
Coincidence degree.

##### 3724 Positive Solutions for Systems of Nonlinear Third-Order Differential Equations with p-Laplacian

**Authors:**
Li Xiguang

**Abstract:**

**Keywords:**
p-Laplacian,
cone,
fixed point theorem,
positive
solution.

##### 3723 Almost Periodic Solution for a Food-limited Population Model with Delay and Feedback Control

**Authors:**
Xiaoyan Dou,
Yongkun Li

**Abstract:**

In this paper, we consider a food-limited population model with delay and feedback control. By applying the comparison theorem of the differential equation and constructing a suitable Lyapunov functional, sufficient conditions which guarantee the permanence and existence of a unique globally attractive positive almost periodic solution of the system are obtained.

**Keywords:**
Almost periodic solution,
food-limited population,
feedback control,
permanence.

##### 3722 Almost Periodicity in a Harvesting Lotka-Volterra Recurrent Neural Networks with Time-Varying Delays

**Authors:**
Yongzhi Liao

**Abstract:**

By using the theory of exponential dichotomy and Banach fixed point theorem, this paper is concerned with the problem of the existence and uniqueness of positive almost periodic solution in a delayed Lotka-Volterra recurrent neural networks with harvesting terms. To a certain extent, our work in this paper corrects some result in recent years. Finally, an example is given to illustrate the feasibility and effectiveness of the main result.

**Keywords:**
positive almost periodic solution,
Lotka-Volterra,
neural
networks,
Banach fixed point theorem,
harvesting

##### 3721 n-Butanol as an Extractant for Lactic Acid Recovery

**Authors:**
Kanungnit Chawong,
Panarat Rattanaphanee

**Abstract:**

Extraction of lactic acid from aqueous solution using n-butanol as an extractant was studied. Effect of mixing time, pH of the aqueous solution, initial lactic acid concentration, and volume ratio between the organic and the aqueous phase were investigated. Distribution coefficient and degree of lactic acid extraction was found to increase when the pH of aqueous solution was decreased. The pH Effect was substantially pronounced at pH of the aqueous solution less than 1. Initial lactic acid concentration and organic-toaqueous volume ratio appeared to have positive effect on the distribution coefficient and the degree of extraction. Due to the nature of n-butanol that is partially miscible in water, incorporation of aqueous solution into organic phase was observed in the extraction with large organic-to-aqueous volume ratio.

**Keywords:**
Lactic acid,
liquid-liquid extraction,
n-Butanol,
Solvating extractant.

##### 3720 A Special Algorithm to Approximate the Square Root of Positive Integer

**Authors:**
Hsian Ming Goo

**Abstract:**

The paper concerns a special approximate algorithm of the square root of the specific positive integer, which is built by the use of the property of positive integer solution of the Pell’s equation, together with using some elementary theorems of matrices, and then takes it to compare with general used the Newton’s method and give a practical numerical example and error analysis; it is unexpected to find its special property: the significant figure of the approximation value of the square root of positive integer will increase one digit by one. It is well useful in some occasions.

**Keywords:**
Special approximate algorithm,
square root,
Pell’s
equation,
Newton’s method,
error analysis.

##### 3719 A Survey on Positive Real and Strictly Positive Real Scalar Transfer Functions

**Authors:**
Mojtaba Hakimi-Moghaddam

**Abstract:**

**Keywords:**
Real rational transfer functions,
positive realness property,
strictly positive realness property,
equivalent conditions.

##### 3718 Positive Periodic Solutions for a Predator-prey Model with Modified Leslie-Gower Holling-type II Schemes and a Deviating Argument

**Authors:**
Yanling Zhu,
Kai Wang

**Abstract:**

In this paper, by utilizing the coincidence degree theorem a predator-prey model with modified Leslie-Gower Hollingtype II schemes and a deviating argument is studied. Some sufficient conditions are obtained for the existence of positive periodic solutions of the model.

**Keywords:**
Predator-prey model,
Holling II type functional response,
positive periodic solution,
coincidence degree theorem.

##### 3717 An Asymptotic Solution for the Free Boundary Parabolic Equations

**Authors:**
Hsuan-Ku Liu,
Ming Long Liu

**Abstract:**

In this paper, we investigate the solution of a two dimensional parabolic free boundary problem. The free boundary of this problem is modelled as a nonlinear integral equation (IE). For this integral equation, we propose an asymptotic solution as time is near to maturity and develop an integral iterative method. The computational results reveal that our asymptotic solution is very close to the numerical solution as time is near to maturity.

**Keywords:**
Integral equation,
asymptotic solution,
free boundary problem,
American exchange option.

##### 3716 Permanence and Almost Periodic Solutions to an Epidemic Model with Delay and Feedback Control

**Authors:**
Chenxi Yang,
Zhouhong Li

**Abstract:**

This paper is concerned with an epidemic model with delay. By using the comparison theorem of the differential equation and constructing a suitable Lyapunov functional, Some sufficient conditions which guarantee the permeance and existence of a unique globally attractive positive almost periodic solution of the model are obtain. Finally, an example is employed to illustrate our result.

**Keywords:**
Permanence,
Almost periodic solution,
Epidemic
model,
Delay,
Feedback control.

##### 3715 On the Approximate Solution of a Nonlinear Singular Integral Equation

**Authors:**
Nizami Mustafa,
C. Ardil

**Abstract:**

In this study, the existence and uniqueness of the solution of a nonlinear singular integral equation that is defined on a region in the complex plane is proven and a method is given for finding the solution.

**Keywords:**
Approximate solution,
Fixed-point principle,
Nonlinear singular integral equations,
Vekua integral operator

##### 3714 Laplace Decomposition Approximation Solution for a System of Multi-Pantograph Equations

**Authors:**
M. A. Koroma,
C. Zhan,
A. F. Kamara,
A. B. Sesay

**Abstract:**

In this work we adopt a combination of Laplace transform and the decomposition method to find numerical solutions of a system of multi-pantograph equations. The procedure leads to a rapid convergence of the series to the exact solution after computing a few terms. The effectiveness of the method is demonstrated in some examples by obtaining the exact solution and in others by computing the absolute error which decreases as the number of terms of the series increases.

**Keywords:**
Laplace decomposition,
pantograph equations,
exact
solution,
numerical solution,
approximate solution.

##### 3713 Periodic Solutions for a Two-prey One-predator System on Time Scales

**Authors:**
Changjin Xu

**Abstract:**

In this paper, using the Gaines and Mawhin,s continuation theorem of coincidence degree theory on time scales, the existence of periodic solutions for a two-prey one-predator system is studied. Some sufficient conditions for the existence of positive periodic solutions are obtained. The results provide unified existence theorems of periodic solution for the continuous differential equations and discrete difference equations.

**Keywords:**
Time scales,
competitive system,
periodic solution,
coincidence degree,
topological degree.

##### 3712 Tree Sign Patterns of Small Order that Allow an Eventually Positive Matrix

**Authors:**
Ber-Lin Yu,
Jie Cui,
Hong Cheng,
Zhengfeng Yu

**Abstract:**

**Keywords:**
Eventually positive matrix,
sign pattern,
tree.

##### 3711 Solution of Fuzzy Differential Equation under Generalized Differentiability by Genetic Programming

**Authors:**
N. Kumaresan,
J. Kavikumar,
M. Kumudthaa,
Kuru Ratnavelu

**Abstract:**

**Keywords:**
Fuzzy differential equation,
Generalized differentiability,
Genetic programming and H-difference.

##### 3710 Online Web Service based Solution for Urban Traffic Management

**Authors:**
A. Ionita,
A. Zafiu,
C. Ghita

**Abstract:**

**Keywords:**
navigation,
real time,
route,
traffic pursuit,
webservice.

##### 3709 Thermodynamic Study for Aggregation Behavior of Hydrotropic Solution

**Authors:**
Meghal Desai,
Jigisha Parikh

**Abstract:**

Aggregation behavior of sodium salicylate and sodium cumene sulfonate was studied in aqueous solution at different temperature. Specific conductivity and relative viscosity were measured at different temperature to find minimum hydrotropic concentration. The thermodynamic parameters (free energy, enthalpy and entropy) were evaluated in the temperature range of 30°C-70°C. The free energy decreased with increase in temperature. The aggregation was found to be exothermic in nature and favored by positive value of entropy.

**Keywords:**
Hydrotropes,
Enthalpy,
Entropy,
Free Energy,
Minimum Hydrotropic Concentration.