Abstract
In this paper, by employing fixed point index theory and Leray-Schauder degree theory, we obtain the existence and multiplicity of sign-changing solutions for nonlinear second-order differential equations with integral boundary value conditions.
Highlights
We are concerned with the existence of sign-changing solutions for the following nonlinear second-order integral boundary-value problem (BVP for short) x′′(t) + f (x(t)) = 0, 0 ≤ t ≤ 1
Boundary-value problems with integral boundary conditions for ordinary differential equations arise in different fields of applied mathematics and physics such as heat conduction, chemical engineering, underground water flow, thermo-elasticity, and plasma physics
Motivated by [11], [17], [19], [21], [22], the purpose of this paper is to investigate sign-changing solutions for BVP (1) following the method formulated by Xu in [24]
Summary
Many researchers have studied positive solutions for multi-point boundary value problems, and obtained sufficient conditions for existence, see [4, 5, 6, 15, 28] and the references therein. In [21, 22], Webb and Infante used fixed point index theory and formulated a general method for solving problems with integral boundary conditions of Riemann-Stieltjes type. By using fixed point index theory, under some suitable conditions, they obtained some existence results for multiple solutions including sign-changing solutions. Utilizing the fixed point index theory and computing eigenvalues and the algebraic multiplicity of the corresponding linear operator, Li and Li [11] obtained some existence results for sign-changing solutions for the following integral boundary-value problem (3).
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