科研之友
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摘要
We consider a nonlinear Dirichlet elliptic equation driven by a nonhomogeneous differential operator and with a Caratheodory reaction f(z, zeta), whose primitive f(z, zeta) is p-superlinear near +/-infinity, but need not satisfy the usual in such cases, the Ambrosetti-Rabinowitz condition. Using a combination of variational methods with the Morse theory (critical groups), we show that the problem has at least three nontrivial smooth solutions. Our result unifies the study of %26quot;superlinear%26quot; equations monitored by some differential operators of interest like the p-Laplacian, the (p, q)-Laplacian, and the p-generalized mean curvature operator.
- 出版日期2012
