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摘要
We consider a class of particular -Laplacian Dirichlet problems with a right-hand side nonlinearity which exhibits an asymmetric growth at +a and -a. Namely, it is linear at -a and superlinear at +a. 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 . 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 .
