Ruichang Pei, Jihui Zhang
Abstract:
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 email: prc211@163.com | |
Jihui Zhang School of Mathematics and Computer Sciences Nanjing, Normal University Nanjing 210097, China email: zhangjihui@njnu.edu.cn |
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