| Title:
|
Semilinear elliptic problems with nonlinearities depending on the derivative (English) |
| Author:
|
Arcoya, David |
| Author:
|
del Toro, Naira |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
44 |
| Issue:
|
3 |
| Year:
|
2003 |
| Pages:
|
413-426 |
| . |
| Category:
|
math |
| . |
| Summary:
|
We deal with the boundary value problem $$ \alignat2 -\Delta u(x) & = \lambda _{1}u(x)+g(\nabla u(x))+h(x), \quad && x\in \Omega \ u(x) & = 0, && x\in \partial \Omega \endalignat $$ where $\Omega \subset \Bbb R^N$ is an smooth bounded domain, $\lambda _{1}$ is the first eigenvalue of the Laplace operator with homogeneous Dirichlet boundary conditions on $\Omega $, $h\in L^{\max \{2,N/2\}}(\Omega )$ and $g:\Bbb R^N\longrightarrow \Bbb R$ is bounded and continuous. Bifurcation theory is used as the right framework to show the existence of solution provided that $g$ satisfies certain conditions on the origin and at infinity. (English) |
| Keyword:
|
nonlinear boundary value problems |
| Keyword:
|
elliptic partial differential equations |
| Keyword:
|
bifurcation |
| Keyword:
|
resonace |
| MSC:
|
35B32 |
| MSC:
|
35B34 |
| MSC:
|
35J25 |
| MSC:
|
35J60 |
| MSC:
|
35J65 |
| MSC:
|
47J15 |
| idZBL:
|
Zbl 1105.35038 |
| idMR:
|
MR2025810 |
| . |
| Date available:
|
2009-01-08T19:30:14Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119398 |
| . |
| Reference:
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