# American Institute of Mathematical Sciences

March  2008, 7(2): 383-405. doi: 10.3934/cpaa.2008.7.383

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

 1 Department of Applied Mathematics, National University of Kaohsiung, Kaohsiung 811, Taiwan

Received  September 2005 Revised  July 2007 Published  December 2007

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.
Citation: Tsung-Fang Wu. On semilinear elliptic equations involving critical Sobolev exponents and sign-changing weight function. Communications on Pure & Applied Analysis, 2008, 7 (2) : 383-405. doi: 10.3934/cpaa.2008.7.383
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