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A semilinear elliptic problem involving sign-changing weight function

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A semilinear elliptic problem involving sign-changing

weight function

Tsung-fang Wu

Department of Applied Mathematics

National University of Kaohsiung, Kaohsiung 811, Taiwan

Abstract. In this talk, we will consider the combined effects of concave and

convex nonlinearities on the number of nontrivial nonnegative solutions for semilinear elliptic problems involving sign-changing weight function. With the help of the Nehari manifold, we prove that the existence of multiple positive solutions for semilinear elliptic problems.

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