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Semilinear elliptic problems with singular potentials in ℝN

Published online by Cambridge University Press:  14 November 2011

Marino Badiale  and
Nicoletta A. Tchou
Marino Badiale
Affiliation:
Universita degli studi di Padova, Dipartimento di Matematica Pura e Applicata, via Belzoni 7, 35131 Padova, Italy
Nicoletta A. Tchou
Affiliation:
Universita degli studi dell'Aquila, Dipartimento di Matematica- loc. Coppito, 67100 L'Aquila, Italy
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Synopsis

We study a semilinear elliptic problem on ℝN where a potential is not a bounded function but can also be an infinite measure. We analyse the lack of compactness of the problem, obtaining a structure theorem for Palais-Smale sequences. This result allows us to obtain different kinds of existence theorems by a variational approach.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 123 , Issue 4 , 1993 , pp. 593 - 619
Copyright
Copyright © Royal Society of Edinburgh 1993

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