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}
}
  • A. Bahri, P. Lions
  • Published 1997
  • Mathematics
  • 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. 
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