%0 Journal Article
%T The Existence of Countably Many Positive Solutions for Nonlinear nth-Order Three-Point Boundary Value Problems
%A Yude Ji
%A Yanping Guo
%J Boundary Value Problems
%D 2009
%I Springer
%R 10.1155/2009/572512
%X We consider the existence of countably many positive solutions for nonlinear nth-order three-point boundary value problem u(n)(t)+a(t)f(u(t))=0, t¡Ê(0,1), u(0)=¦Áu(¦Ç), u¡ä(0)= =u(n 2)(0)=0, u(1)=¦Âu(¦Ç), where n¡Ý2,¦Á¡Ý0,¦Â¡Ý0,0<¦Ç<1,¦Á+(¦Â ¦Á)¦Çn 1<1, a(t)¡ÊLp[0,1] for some p¡Ý1 and has countably many singularities in [0,1/2). The associated Green's function for the nth-order three-point boundary value problem is first given, and growth conditions are imposed on nonlinearity f which yield the existence of countably many positive solutions by using the Krasnosel'skii fixed point theorem and Leggett-Williams fixed point theorem for operators on a cone.
%U http://dx.doi.org/10.1155/2009/572512