Periodic solutions of second order nonlinear difference equations with discrete -Laplacian |
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Authors: | C Bereanu HB Thompson |
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Institution: | aDépartement de Mathématique, Université Catholique de Louvain, B-1348 Louvain-la-Neuve, Belgium;bDepartment of Mathematics, University of Queensland, Brisbane, Queensland 4072, Australia |
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Abstract: | We use Brouwer degree to prove existence and multiplicity results for the periodic solutions of some nonlinear second order difference equations involving discrete -Laplacian. We obtain in particular upper and lower solutions theorems, Ambrosetti–Prodi type multiplicity results, sharp existence conditions for nonlinearities which are bounded from below or from above and necessary and sufficient conditions for the existence of positive periodic solutions when the nonlinearity is singular at 0. |
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Keywords: | Nonlinear difference equations Discrete sciencedirect com/scidirimg/entities/3d5 -Laplacian" target="_blank">gif" alt="phi" title="phi" border="0">-Laplacian Brouwer degree |
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