Geodesic
Multiple positive solutions for a critical elliptic problem with concave and convex nonlinearities
Electronic journal of differential equations, Tome 2014 (2014)
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.
Classification : 35J20, 58J05
Keywords: Nehari manifold, critical Sobolev exponent, positive solution, semi-linear elliptic problem, Ljusternik-Schnirelmann category 
@article{EJDE_2014__2014__a134,
     author = {Fan,  Haining},
     title = {Multiple positive solutions for a critical elliptic problem with concave and convex nonlinearities},
     journal = {Electronic journal of differential equations},
     year = {2014},
     volume = {2014},
     zbl = {1291.35076},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a134/}
}
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%0 Journal Article
%A Fan,  Haining
%T Multiple positive solutions for a critical elliptic problem with concave and convex nonlinearities
%J Electronic journal of differential equations
%D 2014
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%F EJDE_2014__2014__a134
Fan,  Haining. Multiple positive solutions for a critical elliptic problem with concave and convex nonlinearities. Electronic journal of differential equations, Tome 2014 (2014). http://geodesic.mathdoc.fr/item/EJDE_2014__2014__a134/