Electron. J. Diff. Equ., Vol. 2014 (2014), No. 82, pp. 1-14.

Multiple positive solutions for a critical elliptic problem with concave and convex nonlinearities

Haining Fan

In this article, we study the multiplicity of positive solutions for a semi-linear elliptic problem involving critical Sobolev exponent and concave-convex nonlinearities. With the help of Nehari manifold and Ljusternik-Schnirelmann category, we prove that problem admits at least cat$(\Omega)+1$ positive solutions.

Submitted January 18, 2013. Published March 26, 2014.
Math Subject Classifications: 35J20, 58J05.
Key Words: Nehari manifold; critical Sobolev exponent; positive solution; semi-linear elliptic problem; Ljusternik-Schnirelmann category.

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Haining Fan
College of Sciences
China University of Mining and Technology
Xuzhou 221116, China
email: fanhaining888@163.com

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