GALERKIN-TYPE MINIMIZERS TO A COMPETING PROBLEM FOR ((Formula presented))-LAPLACIAN WITH VARIABLE EXPONENTS

This study focuses on a sequence of approximate minimizers for the functional J(U)=integral(ohm) Sigma(N)(I=1) 1/Pi(x)|phi=|partial derivative u/(pi(x))(partial derivative xi:) (dx-& micro; integral ohm) Sigma(N)(I=1) 1/qi(x)|phi=|partial derivative u/(partial derivative x)|(qi(x)) dx-integral F-Omega (u (x) dx, where ohm C R-N (N > 3) is a bounded domain, and p(i), q(i is an element of) C(ohm) with 1 < p(i,) q(i) <+infinity for all i is an element of {1,. .. , N}. We establish the convergence result to the infimum of J(u) when F : R--> R is a locally Lipschitz function of controlled growth, following the Galerkin method. As an application, we establish the existence of solutions to a class of Dirichlet inclusions associated to the functional.