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