Ruichang Pei, Jihui Zhang
We consider the elliptic equation
where and for all . The nonlinear term exhibits an asymmetric growth at and in . Namely, it is linear at and superlinear at . However, it need not satisfy the Ambrosetti-Rabinowitz condition on the positive semiaxis. Some existence results for nontrivial solution are established by using the minimax methods combined with the improved Moser-Trudinger inequality.
Submitted October 5, 2014. Published December 4, 2014.
Math Subject Classifications: 35J60, 35J20, 35B38.
Key Words: Schrodinger equation; asymmetric problems; one side resonance; subcritical exponential growth.
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| Ruichang Pei |
School of Mathematics and Statistics
Tianshui Normal University
Tianshui 741001, China
| Jihui Zhang |
School of Mathematics and Computer Sciences
Nanjing, Normal University
Nanjing 210097, China
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