Existence of solutions of nonlocal perturbations of dirichlet discrete nonlinear problems |
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Authors: | Alberto CABADA Nikolay D. DIMITROV |
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Affiliation: | Instituto de Matemáticas, Facultade de Matemáticas, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain;Department of Mathematical Analysis, University of Rousse, 7017 Rousse, Bulgaria |
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Abstract: | This paper is devoted to the study of second order nonlinear difference equations. A Nonlocal Perturbation of a Dirichlet Boundary Value Problem is considered. An exhaustive study of the related Green's function to the linear part is done. The exact expression of the function is given, moreover the range of parameter for which it has constant sign is obtained. Using this, some existence results for the nonlinear problem are deduced from monotone iterative techniques, the classical Krasnoselski fixed point theorem or by application of recent fixed point theorems that combine both theories. |
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Keywords: | Dirichlet boundary value problem nonlocal perturbations Green's function parameter dependence 39A10 39A06 39A70 |
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