The Solvability of Concave-Convex Quasilinear Elliptic Systems Involving $p$-Laplacian and Critical Sobolev Exponent
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Abstract:
In this work, we study the existence of non-trivial multiple solutions for a class of quasilinear elliptic systems equipped with concave-convex nonlinearities and critical growth terms in bounded domains. By using the variational method, especially Nehari manifold and Palais-Smale condition, we prove the existence and multiplicity results of positive solutions.
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Journal title
volume 12 issue 1
pages 39- 57
publication date 2018-11-01
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