Existence and multiplicity of solutions to even order ordinary differential equations via variational methods |
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Authors: | Liu Yang Haibo Chen |
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Affiliation: | 1. Department of Mathematics, Central South University, Changsha, Hunan 410075, PR China;2. Department of Mathematics, Hengyang Normal University, Hengyang, Hunan 421008, PR China |
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Abstract: | In this paper, we study the existence and multiplicity of solutions for two-point boundary value problems for even order ordinary differential equation. By using the critical point theory and the property of projective operator, we establish some conditions on the nonlinearity which guarantee that the nonlinear Hammerstein integral equation with quasi-positive definite kernel has at least one solution, two nontrivial solutions and finite pairs of solutions, respectively. As an application, we get the corresponding results for two-point boundary value problems for even order ordinary differential equation. Moreover, an example is presented to illustrate our main results. |
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