We consider the existence of ground states for the problem Delta u + K(\x\)U-(n+2/(n-2)) = 0 where K(\x\) is a positive, bounded, continuous function. We use dynamical systems methods, especially the method of the Melnikov function to find conditions under which this problem admits a ground state or a singular ground state. The sensitivity of positive solutions depending on K(\x\) is discussed for non-monotone K.
Melnikov method and elliptic equations with critical exponent / R. Johnson; X.-B. Pan; Y.-F. Yi. - In: INDIANA UNIVERSITY MATHEMATICS JOURNAL. - ISSN 0022-2518. - STAMPA. - 43:(1994), pp. 1045-1077. [10.1512/iumj.1994.43.43046]
Melnikov method and elliptic equations with critical exponent
JOHNSON, RUSSELL ALLAN;
1994
Abstract
We consider the existence of ground states for the problem Delta u + K(\x\)U-(n+2/(n-2)) = 0 where K(\x\) is a positive, bounded, continuous function. We use dynamical systems methods, especially the method of the Melnikov function to find conditions under which this problem admits a ground state or a singular ground state. The sensitivity of positive solutions depending on K(\x\) is discussed for non-monotone K.
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