Solutions of periodic boundary value problems for second-order nonlinear differential equations via variational methods |
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Authors: | Zhiqing Han |
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Institution: | School of Mathematical Sciences, Dalian University of Technology, Dalian, 116023 Liaoning, PR China |
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Abstract: | By introducing a variational framework for a class of second order nonlinear differential equations with non-separated periodic boundary value conditions, some results on the existence of non-trivial, positive and negative solutions of the problems are obtained. Some results by Atici-Guseinov, Graef-Kong, etc. obtained by topological degree methods are extended. The resonant case of the problems where the nonlinearities are unbounded and satisfy Ahmad-Lazer-Paul type conditions is also considered. |
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Keywords: | Boundary value problems Periodic solutions Variational methods Eigenvalues |
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