Existence of one weak solution for $p(x)$-biharmonic equations involving a concave-convex nonlinearity

R. A. Mashiyev, G. Alisoy, I. Ekincioglu

In the present paper, using variational approach and the theory of the variable exponent Lebesgue spaces, the existence of nontrivial weak solutions to a fourth order elliptic equation involving a $p(x)$-biharmonic operator and a concave-convex nonlinearity the Navier boundary conditions is obtained.