Article ID Journal Published Year Pages File Type
4622411 Journal of Mathematical Analysis and Applications 2007 18 Pages PDF
Abstract

Necessary and sufficient conditions are obtained for the existence of symmetric positive solutions to the boundary value problem(|u″|p−1u″)″=f(t,u,u′,u″),t∈(0,1),u(2i)(0)=u(2i)(1)=0,i=0,1. Applications of our results to the special case where f is a power function of u and its derivatives are also discussed. Moreover, similar conclusions for a more general higher order boundary value problem are established. Our results extend some recent work in the literature on boundary value problems for ordinary differential equations. The analysis of this paper mainly relies on fixed point theorems on cones.

Related Topics
Physical Sciences and Engineering Mathematics Analysis
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