Nontrivial solution for asymmetric (p,2)-Laplacian Dirichlet problem

被引：0
作者：
Ruichang Pei
Jihui Zhang
机构：
[1] Tianshui Normal University,School of Mathematics and Statistics
[2] Nanjing Normal University,School of Mathematical Sciences, Institute of Mathematics
来源：
Boundary Value Problems | / 2014卷
关键词：
asymmetric Dirichlet problem; subcritical exponential growth; one side resonance;
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摘要：
We consider a class of particular (p,2)-Laplacian Dirichlet problems with a right-hand side nonlinearity which exhibits an asymmetric growth at +∞ and −∞. Namely, it is linear at −∞ and superlinear at +∞. However, it need not satisfy the Ambrosetti-Rabinowitz condition on the positive semi-axis. Some existence results for a nontrivial solution are established by the mountain pass theorem and a variant version of the mountain pass theorem in the general case 2<p<N. Similar results are also established by combining the mountain pass theorem and a variant version of the mountain pass theorem with the Moser-Trudinger inequality in the case of p=N.
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