Abstract
This paper concerns the existence of nontrivial solutions for a boundary value problem with integral boundary conditions by topological degree theory. Here the nonlinear term is a sign-changing continuous function and may be unbounded from below.
Highlights
Consider the following Sturm-Liouville problem with integral boundary conditions ⎧⎪⎨ (Lu)(t) + h(t)f (t, u(t)) =, < t , q(t) ∈ C[, ], q(t)
Our findings presented in this paper have the following new features
It is easy to show that A : E → E is a completely continuous nonlinear operator, and if u ∈ E is a fixed point of A, u is a solution of BVP ( . ) by Lemma
Summary
Consider the following Sturm-Liouville problem with integral boundary conditions. where (Lu)(t) = (p(t)u (t)) + q(t)u(t), p(t) ∈ C [ , ], p(t) > , q(t) ∈ C[ , ], q(t) < , α and β are right continuous on [ , ), left continuous at t = and nondecreasing on [ , ] with α( ) = β( ) = ; γ , γ ∈ [ , π / ], u(τ ) dα(τ ). Consider the following Sturm-Liouville problem with integral boundary conditions. The nonlinear term f : [ , ] × (–∞, +∞) → (–∞, +∞) is a continuous sign-changing function and f may be unbounded from below, h : ( , ) → [ , +∞) with such that ( . ), ( . ) hold and K maps P into P
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