Elliptic equations with one-sided critical growth

We consider elliptic equations in bounded domains $Omegasubset 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