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...
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| Format: | Article |
| Language: | English |
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Texas State University
1997-07-01
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| Series: | Electronic Journal of Differential Equations |
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| Online Access: | http://ejde.math.txstate.edu/Volumes/1997/11/abstr.html |
| Summary: | 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 $u$. |
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| ISSN: | 1072-6691 |