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Open Access Research

Existence of solutions for second-order three-point integral boundary value problems at resonance

Hongliang Liu and Zigen Ouyang*

Author Affiliations

School of Nuclear Science and Technology, School of Mathematics and Physics, University of South China, Hengyang, 421001, P.R. China

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Boundary Value Problems 2013, 2013:197  doi:10.1186/1687-2770-2013-197

Published: 3 September 2013

Abstract

A class of second-order three-point integral boundary value problems at resonance is investigated in this paper. Using intermediate value theorems, we obtain a sufficient condition for the existence of the solution for the equation. An example is given to demonstrate our main results.

MSC: 34B10, 34B16, 34B18.

Keywords:
integral boundary value problem; resonance; fixed point theorem; intermediate value theorem