Positive Solutions for Three-Point Boundary Value Problems of Third-Order Nonlinear Singular Differential Equations in Banach Space

Authors: Li Xiguang

Abstract:

In this paper, by constructing a special set and utilizing fixed point index theory, we study the existence of solution for singular differential equation in Banach space, which improved and generalize the result of related paper.

Keywords: Banach space, cone, fixed point index, singular differential equation.

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1335768

References:

[1] Lan K, Webb J L. Positive solutions of semilinear differential equations with singularities. J Diff Eqns, 1998, 148:407-421.
[2] Agarwal R.P, ORegan,D. A note on existence of nonnegative solutions to singular semipositone problem. Nonlinear Anal, 1999,36:615-622.
[3] Xu X. On some results of singular boundary value problem (D). Jinan: Shandong University, 2001.
[4] Liu Y. Twin solutions to singular semipositone problems. J Math Anal Appl, 2003, 286:248-260.
[5] Anderson D. Multiple positive solution for a three-point boundary value problem. Math Comput Modeling, 1998,27:49-57.
[6] Yao Q. Existence of positive solutions for a third-order three-point boundary value problem with semipositone nonlinearity. Journal of Mathematical Research and Exposition, 2003,23:591-596.
[7] Yu huimin, Liu Y. Twin positive solutions for a singular semipositone boundary value problem. Acta Mathematica Scientia 2009 29(A)1233- 1239.
[8] Cui Yujun, Sun Jingxian. Positive solutions for second-order threepoint boundary value problems in Banach spaces.Acta Mathematicae Applicatae Sinica 2011 34(4)743-751.
[9] Krasnoselskii M A. Positive solution of operator eqution. Groningen: Noordhoff,1964.
[10] Potter A. A fixed point theorem for positive k-set contractions. Proc. Edinburgh Math.Soc.1974,19(2):93-102.
[11] Zhou Y M. Positive solution for second-order three-point boundary value problem. Appiied Mathematica ,2005,18(3):446-454.