Existence and multiplicity of solutions for fourth-order boundary value problems with parameters

Abstract: In this paper we study the existence and multiplicity of the solutions for the fourth-order boundary value problem (BVP) , , , where is continuous, and are parameters. By means of the idea of the decomposition of operators shown by Chen [W.Y. Chen, A decomposition problem for operators, Xuebao of Dongbei Renmin University 1 (1957) 95–98], see also [M. Krasnosel''skii, Topological Methods in the Theory of Nonlinear Integral Equations, Gostehizdat, Moscow, 1956], and the critical point theory, we obtain that if the pair is on the curve satisfying , then the above BVP has at least one, two, three, and infinitely many solutions for λ being in different interval, respectively. [Copyright &y& Elsevier]