Du Bois–Reymond Type Lemma and Its Application to Dirichlet Problem with the p(t)–Laplacian on a Bounded Time Scale

This paper is devoted to study the existence of solutions and their regularity in the [Formula: see text] –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 methodo...

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Autores principales: Mawhin, Jean, Skrzypek, Ewa, Szymańska-Dȩbowska, Katarzyna
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2021
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8534737/
https://www.ncbi.nlm.nih.gov/pubmed/34682076
http://dx.doi.org/10.3390/e23101352
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author Mawhin, Jean
Skrzypek, Ewa
Szymańska-Dȩbowska, Katarzyna
author_facet Mawhin, Jean
Skrzypek, Ewa
Szymańska-Dȩbowska, Katarzyna
author_sort Mawhin, Jean
collection PubMed
description This paper is devoted to study the existence of solutions and their regularity in the [Formula: see text] –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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spelling pubmed-85347372021-10-23 Du Bois–Reymond Type Lemma and Its Application to Dirichlet Problem with the p(t)–Laplacian on a Bounded Time Scale Mawhin, Jean Skrzypek, Ewa Szymańska-Dȩbowska, Katarzyna Entropy (Basel) Article This paper is devoted to study the existence of solutions and their regularity in the [Formula: see text] –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. MDPI 2021-10-16 /pmc/articles/PMC8534737/ /pubmed/34682076 http://dx.doi.org/10.3390/e23101352 Text en © 2021 by the authors. https://creativecommons.org/licenses/by/4.0/Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).
spellingShingle Article
Mawhin, Jean
Skrzypek, Ewa
Szymańska-Dȩbowska, Katarzyna
Du Bois–Reymond Type Lemma and Its Application to Dirichlet Problem with the p(t)–Laplacian on a Bounded Time Scale
title Du Bois–Reymond Type Lemma and Its Application to Dirichlet Problem with the p(t)–Laplacian on a Bounded Time Scale
title_full Du Bois–Reymond Type Lemma and Its Application to Dirichlet Problem with the p(t)–Laplacian on a Bounded Time Scale
title_fullStr Du Bois–Reymond Type Lemma and Its Application to Dirichlet Problem with the p(t)–Laplacian on a Bounded Time Scale
title_full_unstemmed Du Bois–Reymond Type Lemma and Its Application to Dirichlet Problem with the p(t)–Laplacian on a Bounded Time Scale
title_short Du Bois–Reymond Type Lemma and Its Application to Dirichlet Problem with the p(t)–Laplacian on a Bounded Time Scale
title_sort du bois–reymond type lemma and its application to dirichlet problem with the p(t)–laplacian on a bounded time scale
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC8534737/
https://www.ncbi.nlm.nih.gov/pubmed/34682076
http://dx.doi.org/10.3390/e23101352
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