Infitely many solutions to the Dirichlet problem for quasilinear elliptic systems involving the p(x) and q(x)-Laplacian

  • Danila Sandra Moschetto Università di Catania
Keywords: Variational principle, p(x)-Laplacian, Dirichlet problem


In this paper we consider the Dirichlet problem involving the p(x) and q(x) -Laplacian of the type
−∆p(x)u = f (u,v) in Ω
−∆q(x)v = g(u,v) in Ω
u = 0 on ∂Ω
v = 0 on ∂Ω

and, by applying a critical point variational principle obtained by Ricceri as a consequence of a more general variational principle, we prove the existence of infinitely many solutions.

Author Biography

Danila Sandra Moschetto, Università di Catania
Department of Mathematics and Computer Science
Viale A. Doria, 6
95125 - Catania, Italy