  We study the existence of nontrivial weak solutions for a class of
generalized $p(x)$-biharmonic equations with singular nonlinearity and Navier
boundary condition. The proofs combine variational and topological arguments.
The approach developed in this paper allows for the treatment of several
classes of singular biharmonic problems with variable growth arising in applied
sciences, including the capillarity equation and the mean curvature problem.

Analysis of PDEs