A perturbation method in critical point theory and applications

@article{Bahri1981APM,
  title={A perturbation method in critical point theory and applications},
  author={A. Bahri and H. Berestycki},
  journal={Transactions of the American Mathematical Society},
  year={1981},
  volume={267},
  pages={1-32}
}
  • A. Bahri, H. Berestycki
  • Published 1981
  • Mathematics
  • Transactions of the American Mathematical Society
  • This paper is concerned with existence and multiplicity results for nonlinear elliptic equations of the type -Au = |u|''_1u + h(x) in P», u = 0 on 3s. Here, s c R^ is smooth and bounded, and h e L2(Q) is given. We show that there exists pN > 1 such that for any p e (\,pN) and any h e L2(I2), the preceding equation possesses infinitely many distinct solutions. The method rests on a characterization of the existence of critical values by means of noncontractibility properties of certain level… CONTINUE READING
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