Positive solutions of nonlinear singular third-order two-point boundary value problem

By Shuhong Li. 2006

93 citations recorded by the source corpus.

Abstract In this paper, we are concerned with the existence of single and multiple positive solutions to the nonlinear singular third-order two-point boundary value problem u ‴ ( t ) + λ a ( t ) f ( u ( t ) ) = 0 , 0 t 1 , u ( 0 ) = u ′ ( 0 ) = u ″ ( 1 ) = 0 , where λ is a positive parameter. Under various assumptions on a and f we establish intervals of the parameter λ which yield the existence of at least one, at least two, and infinitely many positive solutions of the boundary value problem by using Krasnoselskii's fixed point theorem of cone expansion–compression type.

Subfields: Applied Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/fc21853f96be19eef6479757dff09690e6bb4763

Citations in the corpus

• Positive solutions of boundary value problems for nth order ordinary differential equations (2008, unknown): “Since this pioneering works, a lot research has been done in this area [2, 3, 5, 7, 8, 9].”