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Keywords = du Bois–Reymond lemma

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21 pages, 370 KiB  
Article
Du Bois–Reymond Type Lemma and Its Application to Dirichlet Problem with the p(t)–Laplacian on a Bounded Time Scale
by Jean Mawhin, Ewa Skrzypek and Katarzyna Szymańska-Dȩbowska
Entropy 2021, 23(10), 1352; https://doi.org/10.3390/e23101352 - 16 Oct 2021
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Abstract
This paper is devoted to study the existence of solutions and their regularity in the p(t)–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 [...] Read more.
This paper is devoted to study the existence of solutions and their regularity in the p(t)–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. Full article
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