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On a resonant-superlinear elliptic problem

  • M. Cuesta
  • D.G. de Figueiredo
  • P.N. Srikanth
  • 70 Downloads

Abstract.

We start by discussing the solvability of the following superlinear problem \(\) where \(1 < p < \frac{N+1}{N-1}\), \(\Omega \subset \mathbb{R}^N\) is a smooth bounded domain and f satisfies a one-sided Landesman-Lazer condition. We also consider systems of semilinear elliptic equations with nonlinearities of the above form, so exhibiting superlinearity as \(u\to +\infty\) and resonance as \(u\to -\infty\). A priori bounds for the solutions of the equation and the system are obtained by using Hardy-type inequalities . Existence of solutions is then obtained using topological degree arguments.

Keywords

Bounded Domain Elliptic Equation Elliptic Problem Topological Degree Smooth Bounded Domain 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2003

Authors and Affiliations

  • M. Cuesta
    • 1
  • D.G. de Figueiredo
    • 2
  • P.N. Srikanth
    • 3
  1. 1.Université du Littoral ULCO, 50 rue F. Buisson, B.P. 699, 62228 Calais, France (e-mail: cuesta@lmpa.univ-littoral.fr) FR
  2. 2. IMEEC, UNICAMP, Caixa Postal 6065, 13081-970 Campinas-SP, Brazil (e-mail: djairo@ime.unicamp.br) BR
  3. 3. TIFR Center, P.O. Box 1234, 560012 Bangalore, India (e-mail: srikanth@math.tifrbng.res.in) IN

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