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

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.