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摘要
In this paper we consider the semilinear elliptic problem where f is a nonnegative, locally Lipschitz continuous function with r positive zeros, Omega is a smooth bounded domain and lambda > 0 is a parameter. We show that for large enough lambda there exist 2r positive solutions, irrespective of the behavior of f at zero or infinity, provided only that f verifies a suitable non-integrability condition near each of its zeros, thereby generalizing previous known results. The construction of the solutions rely on the sub- and supersolutions method and topological degree arguments, together with the use of a new Liouville theorem which is an extension of recent results to this type of nonlinearities.
- 出版日期2015-9
