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Existence of positive solutions for indefinite semilinear elliptic equations with concave and convex nonlinaerities

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Existence of positive solutions for indefinite

semilinear elliptic equations with concave and convex

nonlinaerities

Tsung-fang Wu

Department of Applied Mathematics

National University of Kaohsiung, Kaohsiung 811, Taiwan

Abstract. In this talk, we will study the decomposition of the Nehari manifold by

exploiting the combination of concave and convex nonlinearities. The result is subsequently used, in conjunction with the Ljusternik-Schnirelmann category and the variational methods, to prove the existence and multiplicity of positive solutions for an indefinite elliptic problem involving critical Sobolev exponent.

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