Existence of Classical Solutions for Nonlinear Elliptic Equations with Gradient Terms

This paper deals with the existence of solutions of the elliptic equation with nonlinear gradient term [Formula: see text] on [Formula: see text] restricted by the boundary condition [Formula: see text] , where [Formula: see text] is a bounded domain in [Formula: see text] with sufficiently smooth b...

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Detalles Bibliográficos
Autores principales: Li, Yongxiang, Ma, Weifeng
Formato: Online Artículo Texto
Lenguaje:English
Publicado: MDPI 2022
Materias:
Article
Acceso en línea:https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9778083/
https://www.ncbi.nlm.nih.gov/pubmed/36554235
http://dx.doi.org/10.3390/e24121829
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author Li, Yongxiang
Ma, Weifeng
author_facet Li, Yongxiang
Ma, Weifeng
author_sort Li, Yongxiang
collection PubMed
description This paper deals with the existence of solutions of the elliptic equation with nonlinear gradient term [Formula: see text] on [Formula: see text] restricted by the boundary condition [Formula: see text] , where [Formula: see text] is a bounded domain in [Formula: see text] with sufficiently smooth boundary [Formula: see text] , [Formula: see text] , and [Formula: see text] is continuous. The existence results of classical solutions and positive solutions are obtained under some inequality conditions on the nonlinearity [Formula: see text] when [Formula: see text] is small or large enough.
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spelling pubmed-97780832022-12-23 Existence of Classical Solutions for Nonlinear Elliptic Equations with Gradient Terms Li, Yongxiang Ma, Weifeng Entropy (Basel) Article This paper deals with the existence of solutions of the elliptic equation with nonlinear gradient term [Formula: see text] on [Formula: see text] restricted by the boundary condition [Formula: see text] , where [Formula: see text] is a bounded domain in [Formula: see text] with sufficiently smooth boundary [Formula: see text] , [Formula: see text] , and [Formula: see text] is continuous. The existence results of classical solutions and positive solutions are obtained under some inequality conditions on the nonlinearity [Formula: see text] when [Formula: see text] is small or large enough. MDPI 2022-12-15 /pmc/articles/PMC9778083/ /pubmed/36554235 http://dx.doi.org/10.3390/e24121829 Text en © 2022 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
Li, Yongxiang
Ma, Weifeng
Existence of Classical Solutions for Nonlinear Elliptic Equations with Gradient Terms
title Existence of Classical Solutions for Nonlinear Elliptic Equations with Gradient Terms
title_full Existence of Classical Solutions for Nonlinear Elliptic Equations with Gradient Terms
title_fullStr Existence of Classical Solutions for Nonlinear Elliptic Equations with Gradient Terms
title_full_unstemmed Existence of Classical Solutions for Nonlinear Elliptic Equations with Gradient Terms
title_short Existence of Classical Solutions for Nonlinear Elliptic Equations with Gradient Terms
title_sort existence of classical solutions for nonlinear elliptic equations with gradient terms
topic Article
url https://www.ncbi.nlm.nih.gov/pmc/articles/PMC9778083/
https://www.ncbi.nlm.nih.gov/pubmed/36554235
http://dx.doi.org/10.3390/e24121829
work_keys_str_mv AT liyongxiang existenceofclassicalsolutionsfornonlinearellipticequationswithgradientterms
AT maweifeng existenceofclassicalsolutionsfornonlinearellipticequationswithgradientterms

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