Abstract
We consider the existence of single and multiple positive solutions for fourth-order Sturm-Liouville boundary value problem in Banach space. The sufficient condition for the existence of single and multiple positive solutions is obtained by fixed theorem of strict set contraction operator in the frame of the ODE technique. Our results significantly extend and improve many known results including singular and nonsingular cases.
Highlights
The boundary value problems (BVPs) for ordinary differential equations play a very important role in both theory and application
We will study the existence of positive solutions for the following fourth-order nonlinear Sturm-Liouville
The aim of this article is to consider the existence of positive solutions for the more general Sturm-Liouville BVP by using the properties of strict set contraction operator
Summary
The boundary value problems (BVPs) for ordinary differential equations play a very important role in both theory and application. We will study the existence of positive solutions for the following fourth-order nonlinear Sturm-Liouville. The aim of this article is to consider the existence of positive solutions for the more general Sturm-Liouville BVP by using the properties of strict set contraction operator. The Sturm-Liouville BVP (1.1) has a positive solution if and only if the following integral-differential boundary value problem has a positive solution of. It follows from the the continuity of S and (H2) that there exists a positive number L such that || f(Sv(t)) ||1 ≤ L for any v Î B. Suppose that E is a Banach space, K ⊂ E is a cone, let Ω1, Ω2 be two bounded open sets of E such that θ Î Ω1, ̄ 1 ⊂ 2.
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