Open Access Research

Existence of positive solutions to a non-positive elastic beam equation with both ends fixed

Haixia Lu1, Li Sun2,3* and Jingxian Sun2

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Author affiliations

1 Department of Teachers Education, Suqian College, Suqian, Jiangsu 223800, P. R. China

2 Department of Mathematics, Jiangsu Normal University, Xuzhou, Jiangsu 221116, P. R. China

3 School of Mechanics and Civil Engineering, China University of Mining & Technology, Xuzhou, Jiangsu 221008, P. R. China

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Citation and License

Boundary Value Problems 2012, 2012:56 doi:10.1186/1687-2770-2012-56

Published: 14 May 2012

Abstract

This article is concerned with the existence of nontrivial solutions for a non-positive fourth-order two-point boundary value problem (BVP) and the existence of positive solutions for a semipositive fourth-order two-point BVP. In mechanics, the problem describes the deflection of an elastic beam rigidly fixed at both ends. The method to show our main results is the topological degree and fixed point theory of nonlinear operator on lattice.

Mathematics Subject Classification 2010: 34B18; 34B16; 34B15.

Keywords:
lattice; topological degree; fixed point; nontrivial solutions and positive solutions; elastic beam equations