Existence of weak solutions for some quasilinear degenerated elliptic systems in weighted Sobolev spaces

• El Houcine, Rami ^[1] ; Elhoussine , Azroul ; Abdelkrim, Barbara ^[1]
  1. [1] Sidi Mohammed Ben Abdellah University.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 41, Nº. 6, 2022, págs. 1523-1549
• Idioma: inglés
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• Resumen

  • We consider, for a bounded open domain Ω in Rn; (n ≥ 1) and a function u : Ω → ℝm; (m ≥ 1) the quasilinear elliptic system:

      (0.1) Which is a Dirichlet problem. Here, v belongs to the dual space , f and g satisfy some stan- dard continuity and growth conditions. we will show the existence of a weak solution of this problem in the four following cases: σ is mono- tonic, σ is strictly monotonic, σ is quasi montone and σ derives from a convex potential.