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Positive solutions of nonlinear elliptic equations with critical Sobolev exponent and mixed boundary conditions

Published online by Cambridge University Press:  14 November 2011

Massimo Grossi  and
Filomena Pacella
Massimo Grossi
Affiliation:
SISSA, Strada costiera 11, 34014 Trieste, Italy
Filomena Pacella
Affiliation:
Dipartimento di Matematica, Università di Roma “La Sapienza”, P. le A. Moro 2, 00185 Rome, Italy
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Synopsis

In this paper we characterise the levels of the functional (0.3) at which the Palais-Smale condition fails in the Sobolev space V(Ω) defined below. From this result we deduce an existence theorem for positive solutions to the mixed boundary problem (0.1)–(0.2) under geometrical assumptions on the domain Ω and the part of the boundary of Ω where a Neumann condition is prescribed.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 116 , Issue 1-2 , 1990 , pp. 23 - 43
Copyright
Copyright © Royal Society of Edinburgh 1990

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