Existence of solutions for quasilinear parabolic equations at resonance
In this article, we show the existence of nontrivial solutions for a class of quasilinear parabolic differential equations. To obtain the solution in a weighted Sobolev space, we use the Galerkin method, Brouwer's theorem, and a compact Sobolev-type embedding theorem proved by Shapiro.
| Main Authors: | , , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
2013-01-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/2013/13/abstr.html |
| _version_ | 1818826773934112768 |
|---|---|
| author | Gao Jia Xiao-Juan Zhang Li-Na Huang |
| author_facet | Gao Jia Xiao-Juan Zhang Li-Na Huang |
| author_sort | Gao Jia |
| collection | DOAJ |
| description | In this article, we show the existence of nontrivial solutions for a class of quasilinear parabolic differential equations. To obtain the solution in a weighted Sobolev space, we use the Galerkin method, Brouwer's theorem, and a compact Sobolev-type embedding theorem proved by Shapiro. |
| first_indexed | 2024-12-19T00:33:00Z |
| format | Article |
| id | doaj.art-e90e4ffd24e54cdfaccad04b96074285 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-12-19T00:33:00Z |
| publishDate | 2013-01-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-e90e4ffd24e54cdfaccad04b960742852022-12-21T20:45:00ZengTexas State UniversityElectronic Journal of Differential Equations1072-66912013-01-01201313,116Existence of solutions for quasilinear parabolic equations at resonanceGao JiaXiao-Juan ZhangLi-Na HuangIn this article, we show the existence of nontrivial solutions for a class of quasilinear parabolic differential equations. To obtain the solution in a weighted Sobolev space, we use the Galerkin method, Brouwer's theorem, and a compact Sobolev-type embedding theorem proved by Shapiro.http://ejde.math.txstate.edu/Volumes/2013/13/abstr.htmlWeighted Sobolev spacequasilinear parabolic equationresonance |
| spellingShingle | Gao Jia Xiao-Juan Zhang Li-Na Huang Existence of solutions for quasilinear parabolic equations at resonance Electronic Journal of Differential Equations Weighted Sobolev space quasilinear parabolic equation resonance |
| title | Existence of solutions for quasilinear parabolic equations at resonance |
| title_full | Existence of solutions for quasilinear parabolic equations at resonance |
| title_fullStr | Existence of solutions for quasilinear parabolic equations at resonance |
| title_full_unstemmed | Existence of solutions for quasilinear parabolic equations at resonance |
| title_short | Existence of solutions for quasilinear parabolic equations at resonance |
| title_sort | existence of solutions for quasilinear parabolic equations at resonance |
| topic | Weighted Sobolev space quasilinear parabolic equation resonance |
| url | http://ejde.math.txstate.edu/Volumes/2013/13/abstr.html |
| work_keys_str_mv | AT gaojia existenceofsolutionsforquasilinearparabolicequationsatresonance AT xiaojuanzhang existenceofsolutionsforquasilinearparabolicequationsatresonance AT linahuang existenceofsolutionsforquasilinearparabolicequationsatresonance |