Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4622411 | Journal of Mathematical Analysis and Applications | 2007 | 18 Pages |
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.
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
John R. Graef, Lingju Kong,