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

Authors: Li Xiguang

Abstract:

In this paper, by constructing a special non-empty closed convex set and utilizing M¨onch fixed point theory, we investigate the existence of solution for a class of fourth-order singular differential equation in Banach space, which improved and generalized the result of related paper.

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

Digital Object Identifier (DOI): doi.org/10.5281/zenodo.1335764

References:

[1] Wei zhengli. Positive solution for a class of fourth-order nonlinear singular boundary value problem. Acta Mathematica Sinica,(chinese series) 2005, 48(4):727-738.
[2] Hao Z C, Liu LS, Debnath L.A necessary and sufficient condition for the existence of positive solutions of fourth-order singular boundary value problems. Appl Math Lett, 2003,16(3):279-285.
[3] Zhang Xinqiu. Existence of positive solution for nonlinear fourthorder singular differential equation with integral boundary conditions in Banach spaces. Acta Mathematica Scientia 2010, 30A(2): 566-575.
[4] Zhang XFeng M, Ge W. Existence results for nonlinear boundary value problems with integral boundary conditions in Banach spaces. Nonlinear Anal, 2008,69: 3310-3321.
[5] Guo D,Lakshmikantham V.Liu X . Nonlinear Integral Equations in Abstract Spaces. Dordrecht: Kluwer Academic Publishers,1996.
[6] Cui Y,Zou Y. Positive solutions of nonlinear singular boundary value problems in abstract spaces. Nonlinear Anal, 2008, 69: 287-294.
[7] Liu L. Iterative method for solutions and coupled quasi-solutions of nonlinear Fredholm integral equations in ordered Banach spaces. Indian J Pure Appl Math, 1996, 27: 959-972.