On the superlinear problems involving p(x)p(x)-Laplacian-like operators without AR-condition

In the present paper, in view of the variational approach, we discuss the nonlinear eigenvalue problems for p(x)p(x)-Laplacian-like operators, originated from a capillary phenomenon. Under some suitable conditions, we prove the existence of nontrivial solutions of the system for every parameter λ>0λ>0.