Existence and blow up of solutions for m ( x )- biharmonic equation with variable exponent sources

In this work concerned with the existence and blow up of solutions for m (x) - biharmonic equation with variable exponent sources. Under appropriate conditions, we discuss the stationary problem and potential wells. By using the Faedo-Galerkin method, we prove the global existence of the solution. We also investigate the blow up of solutions with negative initial energy.