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

Abstract

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.