Existence Of Three Solutions For A Class Of Quasilinear Elliptic Systems Involving The (p(x),q(x))-Laplacian

The author deals with a elliptic systems involving(p(x),q(x))-Laplacian in a nonempty smooth bounded open domainΩ.With different assumptions between p(x),q(x) and N and some reasonable assumptions and growth conditions on nonlinearities, the existences of three solutions that are of the same systems under different conditions is obtained by using three-critical-points theorem obtained by B.Ric-ceri (Nonlinear Analysis 70(2009) 3084-3089) in variable exponent Sobolev spaces W₀^1,p(x)(Ω)×W₀⁽1,q(x)(Ω).