We consider a semilinear elliptic system with both concave-convex nonlinearities and critical growth terms in bounded domains. The existence and multiplicity results of positive solutions are obtained by variational methods.
The multiple results of positive solutions for the following quasilinear elliptic equation: in on , are established. Here, is a bounded smooth domain in denotes the -Laplacian operator, is a positive real parameter, and are continuous functions on which are somewhere positive but which may change sign on . The study is based on the extraction of Palais-Smale sequences in the Nehari manifold.
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