On the existence of a positive solution of semilinear elliptic equations in unbounded domains

@article{Bahri1997OnTE,
title={On the existence of a positive solution of semilinear elliptic equations in unbounded domains},
author={A. Bahri and P. Lions},
journal={Annales De L Institut Henri Poincare-analyse Non Lineaire},
year={1997},
volume={14},
pages={365-413}
}

Annales De L Institut Henri Poincare-analyse Non Lineaire

We prove here the existence of a positive solution, under general conditions, for semilinear elliptic equations in unbounded domains with a variational structure. The solutions we build cannot be obtained in general by minimization problems. And even if Palais-Smale condition is violated, precise estimates on the losses of compactness are obtained by the concentration-compactness method which enables us to apply the theory of critical points at infinity.