Existence and Uniqueness of Solutions for the <i>p</i>(<i>x</i>)-Laplacian Equation with Convection Term
In this paper, we consider the existence and uniqueness of solutions for a quasilinear elliptic equation with a variable exponent and a reaction term depending on the gradient. Based on the surjectivity result for pseudomonotone operators, we prove the existence of at least one weak solution of such...
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| Format: | Article |
| Language: | English |
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MDPI AG
2020-10-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/8/10/1768 |
| _version_ | 1797551100651372544 |
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| author | Bin-Sheng Wang Gang-Ling Hou Bin Ge |
| author_facet | Bin-Sheng Wang Gang-Ling Hou Bin Ge |
| author_sort | Bin-Sheng Wang |
| collection | DOAJ |
| description | In this paper, we consider the existence and uniqueness of solutions for a quasilinear elliptic equation with a variable exponent and a reaction term depending on the gradient. Based on the surjectivity result for pseudomonotone operators, we prove the existence of at least one weak solution of such a problem. Furthermore, we obtain the uniqueness of the solution for the above problem under some considerations. Our results generalize and improve the existing results. |
| first_indexed | 2024-03-10T15:39:58Z |
| format | Article |
| id | doaj.art-edcd91919a614360a8e602fd25ab56bb |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-10T15:39:58Z |
| publishDate | 2020-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-edcd91919a614360a8e602fd25ab56bb2023-11-20T16:55:45ZengMDPI AGMathematics2227-73902020-10-01810176810.3390/math8101768Existence and Uniqueness of Solutions for the <i>p</i>(<i>x</i>)-Laplacian Equation with Convection TermBin-Sheng Wang0Gang-Ling Hou1Bin Ge2College of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, ChinaCollege of Aerospace and Civil Engineering, Harbin Engineering University, Harbin 150001, ChinaCollege of Mathematical Sciences, Harbin Engineering University, Harbin 150001, ChinaIn this paper, we consider the existence and uniqueness of solutions for a quasilinear elliptic equation with a variable exponent and a reaction term depending on the gradient. Based on the surjectivity result for pseudomonotone operators, we prove the existence of at least one weak solution of such a problem. Furthermore, we obtain the uniqueness of the solution for the above problem under some considerations. Our results generalize and improve the existing results.https://www.mdpi.com/2227-7390/8/10/1768<i>p</i>(<i>x</i>)-Laplacian equationconvection termpseudomonotone operatorsexistence resultsuniqueness |
| spellingShingle | Bin-Sheng Wang Gang-Ling Hou Bin Ge Existence and Uniqueness of Solutions for the <i>p</i>(<i>x</i>)-Laplacian Equation with Convection Term Mathematics <i>p</i>(<i>x</i>)-Laplacian equation convection term pseudomonotone operators existence results uniqueness |
| title | Existence and Uniqueness of Solutions for the <i>p</i>(<i>x</i>)-Laplacian Equation with Convection Term |
| title_full | Existence and Uniqueness of Solutions for the <i>p</i>(<i>x</i>)-Laplacian Equation with Convection Term |
| title_fullStr | Existence and Uniqueness of Solutions for the <i>p</i>(<i>x</i>)-Laplacian Equation with Convection Term |
| title_full_unstemmed | Existence and Uniqueness of Solutions for the <i>p</i>(<i>x</i>)-Laplacian Equation with Convection Term |
| title_short | Existence and Uniqueness of Solutions for the <i>p</i>(<i>x</i>)-Laplacian Equation with Convection Term |
| title_sort | existence and uniqueness of solutions for the i p i i x i laplacian equation with convection term |
| topic | <i>p</i>(<i>x</i>)-Laplacian equation convection term pseudomonotone operators existence results uniqueness |
| url | https://www.mdpi.com/2227-7390/8/10/1768 |
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