Nontrivial Solutions for Asymmetric Kirchhoff Type Problems
We consider a class of particular Kirchhoff type problems with a right-hand side nonlinearity which exhibits an asymmetric growth at +∞ and −∞ in ℝN(N=2,3). Namely, it is 4-linear at −∞ and 4-superlinear at +∞. However, it need not satisfy the Ambrosetti-Rabinowitz condition on the positive semiaxi...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2014-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2014/163645 |
| Summary: | We consider a class of particular Kirchhoff type problems with a right-hand side nonlinearity which exhibits an asymmetric growth
at +∞
and −∞ in ℝN(N=2,3). Namely, it is 4-linear at −∞ and 4-superlinear at +∞. However, it need not satisfy the Ambrosetti-Rabinowitz condition on the positive semiaxis. Some existence results for nontrivial solution are established by combining Mountain Pass Theorem and a variant version of Mountain Pass Theorem with Moser-Trudinger inequality. |
|---|---|
| ISSN: | 1085-3375 1687-0409 |