p(x)-biharmonic equations involving (h,r(x))-Hardy singular coefficients with no-flux boundary conditions

In this article, we investigate p (x) -biharmonic equations involving two kinds of different Hardy potentials, in which the r (x) -Hardy potentials are seldom mentioned in previous papers. New criteria for the existence of generalized solutions are reestablished when the nonlinear terms satisfying appropriate assumptions. The results are based on variational methods and the theory of variable exponent Sobolev spaces.