Abstract
We consider the existence of single and multiple positive solutions for a second‐order Sturm‐Liouville boundary value problem in a Banach space. The sufficient condition for the existence of positive solution is obtained by the fixed point theorem of strict set contraction operators in the frame of the ODE technique. Our results significantly extend and improve many known results including singular and nonsingular cases.
Highlights
Boundary value problems for ordinary differential equations play a very important role in both theoretical study and practical application in many fields
Let B ⊂ C J, E be bounded and equicontinuous on J, α B t is continuous on J and α u t dt : u ∈ B ≤ α B t dt
It follows from the uniform continuity of G t, s on 0, 1 × 0, 1 that there exists δ > 0 such that
Summary
Boundary value problems for ordinary differential equations play a very important role in both theoretical study and practical application in many fields. They are used to describe a large number of physical, biological, and chemical phenomena. We study the existence of positive solutions for the following second-order nonlinear Sturm-Liouville boundary value problem BVP in a Banach Space E. The aim of this paper is to consider the existence of positive solutions for the more general Sturm-Liouville boundary value problem 1.1 by using the fixed point theorem of strict set contraction operators. We approximate the singular second-order boundary value problem by constructing an integral operator.
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