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Multiplicity results for nonlinear elliptic equations involving critical Sobolev exponent*

Published online by Cambridge University Press:  14 November 2011

A. Capozzi  and
G. Palmieri
A. Capozzi
Affiliation:
Dipartimento di Matematica, Università degli Studi di Bari, Via G. Fortunato, 70125 Bari, Italy
G. Palmieri
Affiliation:
Dipartimento di Matematica, Università degli Studi di Bari, Via G. Fortunato, 70125 Bari, Italy
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Synopsis

In this paper we study the following boundary value problem

where Ω is a bounded domain in Rn, n≧3, x ∈Rn, p* = 2n/(n – 2) is the critical exponent for the Sobolev embedding is a real parameter and f(x, t) increases, at infinity, more slowly than .

By using variational techniques, we prove the existence of multiple solutions to the equations (0.1), in the case when λ belongs to a suitable left neighbourhood of an arbitrary eigenvalue of −Δ, and the existence of at least one solution for any λ sufficiently large.

Type
Research Article
Information
Proceedings of the Royal Society of Edinburgh Section A: Mathematics , Volume 103 , Issue 3-4 , 1986 , pp. 275 - 285
Copyright
Copyright © Royal Society of Edinburgh 1986

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