Haining Fan
Abstract:
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
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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