Abstract
This paper is concerned with the existence, multiplicity, and nonexistence of positive solutions for nonhomogeneous m-point boundary value problems with two parameters. The proof is based on the fixed-point theorem, the upper-lower solutions method, and the fixed-point index.
Highlights
Many authors have studied the existence, nonexistence, and multiplicity of positive solutions for multipoint boundary value problems by using the fixed-point theorem, the fixed point index theory, and the lower and upper solutions method
We refer the readers to the references [ – ]
May be singular at t = and/or t =. They showed that there exists a positive number b* >
Summary
Many authors have studied the existence, nonexistence, and multiplicity of positive solutions for multipoint boundary value problems by using the fixed-point theorem, the fixed point index theory, and the lower and upper solutions method. Let x(t), y(t) be lower and upper solutions, respectively, of ( ) such that ≤ x(t) ≤ y(t). Proof Suppose on the contrary that there exists a sequence {un} of positive solutions of Eq ( ) at (λn, μn) such that (λn, μn) ∈ for all n ∈ N and un → ∞.
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