Communications on Pure and Applied Analysis (CPAA)

On semilinear elliptic equations involving critical Sobolev exponents and sign-changing weight function

Pages: 383 - 405, Volume 7, Issue 2, March 2008      doi:10.3934/cpaa.2008.7.383

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Tsung-Fang Wu - Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung 811, Taiwan (email)

Abstract: In this paper, we study the decomposition of the Nehari manifold via the combination of concave and convex nonlinearities. Furthermore, we use this result to prove that the semilinear elliptic equation with a sign-changing weight function has at least two positive solutions.

Keywords:  Critical Sobolev exponent, Nehari manifold, concave-convex nonlinearities.
Mathematics Subject Classification:  Primary: 35J65; Secondary: 35J20.

Received: September 2005;      Revised: July 2007;      Available Online: December 2007.