Abstract
We study the existence of multiple positive solutions for th-order multipoint boundary value problem. , , , , where , , . We obtained the existence of multiple positive solutions by applying the fixed point theorems of cone expansion and compression of norm type and Leggett-Williams fixed-point theorem. The results obtained in this paper are different from those in the literature.
Highlights
The existence of positive solutions for nth-order multipoint boundary problems has been studied by some authors see 1, 2
There are few papers dealing with the existence of multiple positive solutions for nth-order multipoint boundary value problem
We study the existence of at least two positive solutions associated with the BVP 1.1 by applying the fixed point theorems of cone expansion and compression of norm type if m ≥ 2 and the existence of at least three positive solutions for BVP 1.1 by using Leggett-Williams fixed-point theorem
Summary
The existence of positive solutions for nth-order multipoint boundary problems has been studied by some authors see 1, 2. By using the fixed point theorems of cone expansion and compression of norm type, Yang and Wei in 2 obtained the existence of at least one positive solutions for the BVP 1.1 if m ≥ 2. Hao et al in 5 had discussed the existence of at least two positive solutions for the BVP 1.1 by applying the Krasonse’skii-Guo fixed point theorem on cone expansion and compression if m 1. There are few papers dealing with the existence of multiple positive solutions for nth-order multipoint boundary value problem.
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