| Title:
|
Nonlinear fourth order problems with asymptotically linear nonlinearities (English) |
| Author:
|
Amor Ben Ali, Abir |
| Author:
|
Dammak, Makkia |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
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2464-7136 (online) |
| Volume:
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149 |
| Issue:
|
2 |
| Year:
|
2024 |
| Pages:
|
209-223 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
We investigate some nonlinear elliptic problems of the form $$ \Delta ^{2}v + \sigma (x) v= h(x,v)\quad \mbox {in}\ \Omega ,\quad v=\Delta v=0 \quad \mbox {on}\ \partial \Omega , \eqno ({\rm P}) $$ where $\Omega $ is a regular bounded domain in $\mathbb {R}^{N}$, $N\geq 2$, $\sigma (x)$ a positive function in $L^{\infty }(\Omega )$, and the nonlinearity $h(x,t)$ is indefinite. We prove the existence of solutions to the problem (P) when the function $h(x,t)$ is asymptotically linear at infinity by using variational method but without the Ambrosetti-Rabinowitz condition. Also, we consider the case when the nonlinearities are superlinear and subcritical. (English) |
| Keyword:
|
asymptotically linear |
| Keyword:
|
mountain pass theorem |
| Keyword:
|
biharmonic equation |
| Keyword:
|
Cerami sequence |
| MSC:
|
35A15 |
| MSC:
|
35J35 |
| MSC:
|
35J60 |
| MSC:
|
35J91 |
| DOI:
|
10.21136/MB.2023.0008-22 |
| . |
| Date available:
|
2024-07-10T15:03:55Z |
| Last updated:
|
2024-07-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/152468 |
| . |
| Reference:
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