ON A NONLOCAL p(x)-LAPLACIAN DIRICHLET PROBLEM INVOLVING SEVERAL CRITICAL SOBOLEV-HARDY EXPONENTS.

The aim of this work is to present a result of multiplicity of solutions, in generalized Sobolev spaces, for a non-local elliptic problem with p(x)-Laplace operator containing k distinct critical Sobolev-Hardy exponents combined with singularity points U ... on Ω, where Ω ⊂ ℝN is a bounded domain with 0 ∈ Ω and 1 < p- ≤ p(x) ≤ p+ < N. The real function M is bounded in [0, +∞) and the functions hi (i = 1,...,k) and f are functions whose properties will be given later. To obtain the result we use the Lions' concentration-compactness principle for critical Sobolev-Hardy exponent in the space W01,p(x)(Ω) due to Yu, Fu and Li, and the Fountain Theorem. [ABSTRACT FROM AUTHOR]