Existence of solutions for anisotropic Kirchhoff-Boussinesq equations with exponential growth

This paper investigates the anisotropic version of the Kirchhoff-Boussinesq type problem Delta(2)u - & sum;(4)(i=1)partial derivative/partial derivative x(i)(|partial derivative u/partial derivative x(i)|(pi-2)partial derivative u/partial derivative x(i)) = f(u), in a smooth bounded domain Omega subset of R-4, where 2< p(1), p(2), p(3), p(4) < 4 and f : R -> R is a superlinear continuous class function with exponential subcritical or critical growth. By imposing the boundary condition u = Delta u = 0 on partial derivative Omega and utilizing the Nehari manifold method, the existence of a ground state solution is proven.