Abstract
We study the higher-order boundary value problems. The existence of symmetric positive solutions of the problem is discussed. Our results extend some recent work in the literature. The analysis of this paper mainly relies on the monotone iterative technique.
Highlights
We study the boundary value problem (BVP)
If a function u : [, ] → R is continuous and satisfies u(t) = u( – t) for t ∈ [, ], we say that u(t) is symmetric on [, ]
We intend to fill in such gaps in the literature
Summary
If a function u : [ , ] → R is continuous and satisfies u(t) = u( – t) for t ∈ [ , ], we say that u(t) is symmetric on [ , ]. By a symmetric positive solution of BVP P = u ∈ E : u( ) ≥ , u(t) > for t ∈ ( , ), u(t) = u( – t) and there exists constant lu ∈ ( , ) satisfying lue (t) ≤ u(t) ≤ lu– e (t) for t ∈ [ , ] .
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