Du Bois–Reymond Type Lemma and Its Application to Dirichlet Problem with the <i>p</i>(<i>t</i>)–Laplacian on a Bounded Time Scale
This paper is devoted to study the existence of solutions and their regularity in the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>(</mo><mi>t</mi><m...
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| Format: | Article |
| Language: | English |
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MDPI AG
2021-10-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/23/10/1352 |
| _version_ | 1827679510014722048 |
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| author | Jean Mawhin Ewa Skrzypek Katarzyna Szymańska-Dȩbowska |
| author_facet | Jean Mawhin Ewa Skrzypek Katarzyna Szymańska-Dȩbowska |
| author_sort | Jean Mawhin |
| collection | DOAJ |
| description | This paper is devoted to study the existence of solutions and their regularity in the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow></semantics></math></inline-formula>–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. |
| first_indexed | 2024-03-10T06:34:20Z |
| format | Article |
| id | doaj.art-0eaabeadeca44215b840e5db2e72edfe |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-10T06:34:20Z |
| publishDate | 2021-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-0eaabeadeca44215b840e5db2e72edfe2023-11-22T18:11:44ZengMDPI AGEntropy1099-43002021-10-012310135210.3390/e23101352Du Bois–Reymond Type Lemma and Its Application to Dirichlet Problem with the <i>p</i>(<i>t</i>)–Laplacian on a Bounded Time ScaleJean Mawhin0Ewa Skrzypek1Katarzyna Szymańska-Dȩbowska2Institut de Recherche en Mathématique et Physique, Université Catholique de Louvain, Chemin du Cyclotron, 2, B-1348 Louvain-la-Neuve, BelgiumInstitute of Mathematics, Lodz University of Technology, Al. Politechniki 10, 93-590 Łódź, PolandInstitute of Mathematics, Lodz University of Technology, Al. Politechniki 10, 93-590 Łódź, PolandThis paper is devoted to study the existence of solutions and their regularity in the <inline-formula><math xmlns="http://www.w3.org/1998/Math/MathML" display="inline"><semantics><mrow><mi>p</mi><mo>(</mo><mi>t</mi><mo>)</mo></mrow></semantics></math></inline-formula>–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.https://www.mdpi.com/1099-4300/23/10/1352du Bois–Reymond lemma<i>p</i>(<i>t</i>)–Laplaciantime scalesvariational methodsdirect variational methodmountain pass lemma |
| spellingShingle | Jean Mawhin Ewa Skrzypek Katarzyna Szymańska-Dȩbowska Du Bois–Reymond Type Lemma and Its Application to Dirichlet Problem with the <i>p</i>(<i>t</i>)–Laplacian on a Bounded Time Scale Entropy du Bois–Reymond lemma <i>p</i>(<i>t</i>)–Laplacian time scales variational methods direct variational method mountain pass lemma |
| title | Du Bois–Reymond Type Lemma and Its Application to Dirichlet Problem with the <i>p</i>(<i>t</i>)–Laplacian on a Bounded Time Scale |
| title_full | Du Bois–Reymond Type Lemma and Its Application to Dirichlet Problem with the <i>p</i>(<i>t</i>)–Laplacian on a Bounded Time Scale |
| title_fullStr | Du Bois–Reymond Type Lemma and Its Application to Dirichlet Problem with the <i>p</i>(<i>t</i>)–Laplacian on a Bounded Time Scale |
| title_full_unstemmed | Du Bois–Reymond Type Lemma and Its Application to Dirichlet Problem with the <i>p</i>(<i>t</i>)–Laplacian on a Bounded Time Scale |
| title_short | Du Bois–Reymond Type Lemma and Its Application to Dirichlet Problem with the <i>p</i>(<i>t</i>)–Laplacian on a Bounded Time Scale |
| title_sort | du bois reymond type lemma and its application to dirichlet problem with the i p i i t i laplacian on a bounded time scale |
| topic | du Bois–Reymond lemma <i>p</i>(<i>t</i>)–Laplacian time scales variational methods direct variational method mountain pass lemma |
| url | https://www.mdpi.com/1099-4300/23/10/1352 |
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