Solutions to perturbed eigenvalue problems of the p-Laplacian in R<sup><small>N</small></sup>
Using a variational approach, we investigate the existence of solutions for non-autonomous perturbations of the p-Laplacian eigenvalue problem $$ -Delta _pu=f(x,u)quad { m in}quad {Bbb R}^N,. $$ Under the assumptions that the primitive $F(x,u)$ of $f(x,u)$ interacts only with the first eigenvalue, w...
| Main Author: | |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Texas State University
1997-07-01
|
| Series: | Electronic Journal of Differential Equations |
| Subjects: | |
| Online Access: | http://ejde.math.txstate.edu/Volumes/1997/11/abstr.html |
| _version_ | 1811247044519526400 |
|---|---|
| author | Joao Marcos Do O |
| author_facet | Joao Marcos Do O |
| author_sort | Joao Marcos Do O |
| collection | DOAJ |
| description | Using a variational approach, we investigate the existence of solutions for non-autonomous perturbations of the p-Laplacian eigenvalue problem $$ -Delta _pu=f(x,u)quad { m in}quad {Bbb R}^N,. $$ Under the assumptions that the primitive $F(x,u)$ of $f(x,u)$ interacts only with the first eigenvalue, we look for solutions in the space $D^{1,p}({Bbb R}^N)$. Furthermore, we assume a condition that measures how different the behavior of the function $F(x,u)$ is from that of the $p$-power of $u$. |
| first_indexed | 2024-04-12T15:02:33Z |
| format | Article |
| id | doaj.art-bb268ed72faa4a6fa25e0f5ed477f6e3 |
| institution | Directory Open Access Journal |
| issn | 1072-6691 |
| language | English |
| last_indexed | 2024-04-12T15:02:33Z |
| publishDate | 1997-07-01 |
| publisher | Texas State University |
| record_format | Article |
| series | Electronic Journal of Differential Equations |
| spelling | doaj.art-bb268ed72faa4a6fa25e0f5ed477f6e32022-12-22T03:28:02ZengTexas State UniversityElectronic Journal of Differential Equations1072-66911997-07-01199711115Solutions to perturbed eigenvalue problems of the p-Laplacian in R<sup><small>N</small></sup>Joao Marcos Do OUsing a variational approach, we investigate the existence of solutions for non-autonomous perturbations of the p-Laplacian eigenvalue problem $$ -Delta _pu=f(x,u)quad { m in}quad {Bbb R}^N,. $$ Under the assumptions that the primitive $F(x,u)$ of $f(x,u)$ interacts only with the first eigenvalue, we look for solutions in the space $D^{1,p}({Bbb R}^N)$. Furthermore, we assume a condition that measures how different the behavior of the function $F(x,u)$ is from that of the $p$-power of $u$.http://ejde.math.txstate.edu/Volumes/1997/11/abstr.htmlMountain Pass TheoremPalais-Smale ConditionFirst eigenvalue |
| spellingShingle | Joao Marcos Do O Solutions to perturbed eigenvalue problems of the p-Laplacian in R<sup><small>N</small></sup> Electronic Journal of Differential Equations Mountain Pass Theorem Palais-Smale Condition First eigenvalue |
| title | Solutions to perturbed eigenvalue problems of the p-Laplacian in R<sup><small>N</small></sup> |
| title_full | Solutions to perturbed eigenvalue problems of the p-Laplacian in R<sup><small>N</small></sup> |
| title_fullStr | Solutions to perturbed eigenvalue problems of the p-Laplacian in R<sup><small>N</small></sup> |
| title_full_unstemmed | Solutions to perturbed eigenvalue problems of the p-Laplacian in R<sup><small>N</small></sup> |
| title_short | Solutions to perturbed eigenvalue problems of the p-Laplacian in R<sup><small>N</small></sup> |
| title_sort | solutions to perturbed eigenvalue problems of the p laplacian in r sup small n small sup |
| topic | Mountain Pass Theorem Palais-Smale Condition First eigenvalue |
| url | http://ejde.math.txstate.edu/Volumes/1997/11/abstr.html |
| work_keys_str_mv | AT joaomarcosdoo solutionstoperturbedeigenvalueproblemsoftheplaplacianinrsupsmallnsmallsup |