Marta Calanchi & Bernhard Ruf
Abstract:
We consider elliptic equations in bounded domains
with
nonlinearities which have critical growth at
and linear growth
at
,
with
,
the first eigenvalue of the Laplacian.
We prove that such equations have at least two solutions for
certain forcing terms provided
.
In dimensions
an additional lower order growth term
has to be added to the nonlinearity, similarly as in the famous
result of Brezis-Nirenberg for equations with critical growth.
Submitted March 01, 2002. Published October 18, 2002.
Math Subject Classifications: 35J20.
Key Words: Nonlinear elliptic equation, critical growth,
linking structure.
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Marta Calanchi Dip. di Matematica, Universita degli Studi, Via Saldini 50, 20133 Milano, Italy calanchi@mat.unimi.it, ph. +39.02.50316144 |
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Bernhard Ruf Dip. di Matematica, Universita degli Studi, Via Saldini 50, 20133 Milano, Italy e-mail: ruf@mat.unimi.it, ph. +39.02.50316157 |
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