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EXISTENCE AND NON-EXISTENCE FOR SCHR¨ODINGER EQUATIONS INVOLVING CRITICAL SOBOLEV EXPONENTS

Henghui Zou
대한수학회 (The Korean Mathematical Society)|2010.05|대한수학회지 (Journal of the KMS)|제47권 제3호|pp. 547-572

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참고문헌

키워드

existencecritical Sobolev exponentconcentration-compactnessm-Laplacianminimax methodsmountain-pass lemmaSchr¨odinger equations
주제분류수학

초록

We study existence of positive solutions of the classical nonlinear Schr¨odinger equation [수식]In fact, we consider the following more general quasi-linear Schr¨odinger equation [수식]where m ∈ (1, n) is a positive number and [수식]is the corresponding critical Sobolev embedding number in Rn. 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.

Abstract

We study existence of positive solutions of the classical nonlinear Schr¨odinger equation [수식]In fact, we consider the following more general quasi-linear Schr¨odinger equation [수식]where m ∈ (1, n) is a positive number and [수식]is the corresponding critical Sobolev embedding number in Rn. 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.

참고문헌 (17)

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