Electronic Journal of Differential Equations,
Vol. 2002(2002), No. 89, pp. 1-21.
Title: Elliptic equations with one-sided critical growth
Authors: Marta Calanchi (Univ. degli Studi,Milano, Italy)
Bernhard Ruf (Univ. degli Studi,Milano, Italy)
Abstract:
We consider elliptic equations in bounded domains
$\Omega\subset \mathbb{R}^N $ with
nonlinearities which have critical growth at $+\infty$
and linear growth $\lambda$ at $-\infty$, with
$\lambda > \lambda_1$, the first eigenvalue of the Laplacian.
We prove that such equations have at least two solutions for
certain forcing terms provided $N \ge 6$.
In dimensions $N = 3,4,5$ 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.