Mediterranean Journal of Mathematics

, Volume 1, Issue 3, pp 241–267

Existence of Solutions to a Semilinear Elliptic System through Orlicz-Sobolev Spaces

  • Philippe Clément
  • Ben de Pagter
  • Guido Sweers
  • François de Thélin
Original paper

Abstract.

Using Orlicz-Sobolev spaces and a variant of the Mountain-Pass Lemma of Ambrosetti-Rabinowitz we obtain existence of a (positive) solution to a semilinear system of elliptic equations. The admissible nonlinearities are such that the system is superlinear and subcritical. The Orlicz setting used here allows us to consider nonlinearities which are not (asymptotically) pure powers. Moreover, by an interpolation theorem of Boyd we find an elliptic regularity result in Orlicz-Sobolev spaces. A bootstrapping argument implies that the above mentioned solutions are classical.

Mathematics Subject Classification (2000).

Primary 35J50 Secondary 46N20 

Keywords.

Elliptic system Orlicz-Sobolev space Mountain Pass Lemma 

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Copyright information

© Birkhäuser Verlag, Basel 2004

Authors and Affiliations

  • Philippe Clément
    • 1
  • Ben de Pagter
    • 1
  • Guido Sweers
    • 1
  • François de Thélin
    • 2
  1. 1.Delft Institute of Applied MathematicsDelft University of TechnologyDelftThe Netherlands
  2. 2.UMR MIPUniversité Paul Sabatier Toulouse IIIToulouse CedexFrance

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