Du Bois–Reymond Type Lemma and Its Application to Dirichlet Problem with the p(t)–Laplacian on a Bounded Time Scale |
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| Authors: | Jean Mawhin Ewa Skrzypek Katarzyna Szyma&#x;ska-D&#x;bowska |
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| Institution: | 1.Institut de Recherche en Mathématique et Physique, Université Catholique de Louvain, Chemin du Cyclotron, 2, B-1348 Louvain-la-Neuve, Belgium;2.Institute of Mathematics, Lodz University of Technology, Al. Politechniki 10, 93-590 Łódź, Poland; |
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| Abstract: | This paper is devoted to study the existence of solutions and their regularity in the –Laplacian Dirichlet problem on a bounded time scale. First, we prove a lemma of du Bois–Reymond type in time-scale settings. Then, using direct variational methods and the mountain pass methodology, we present several sufficient conditions for the existence of solutions to the Dirichlet problem. |
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| Keywords: | du Bois– Reymond lemma p(t)– Laplacian time scales variational methods direct variational method mountain pass lemma |
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