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EXISTENCE AND NON-EXISTENCE FOR SCHRÖDINGER EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS
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 Title & Authors
EXISTENCE AND NON-EXISTENCE FOR SCHRÖDINGER EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS
Zou, Henghui;
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 Abstract
We study existence of positive solutions of the classical nonlinear Schrdinger equation , u > 0 in . In fact, we consider the following more general quasi-linear Schrodinger equation , u > 0 in , where m (1, n) is a positive number and >, is the corresponding critical Sobolev embedding number in . Under appropriate conditions on the functions V(x), f(x, u) and H(x), existence and non-existence results of positive solutions have been established.
 Keywords
concentration-compactness;critical Sobolev exponent;existence;m-Laplacian;minimax methods;mountain-pass lemma;Schrdinger equations;
 Language
English
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