Infinitely Many Solutions for Semilinear Strongly Degenerate Elliptic Differential Equations with Lack of Symmetry

In this paper, we study the existence of multiple solutions for the boundary value problem

where ΩΩ is a bounded domain with smooth boundary in , where  is odd,  is a non-symmetric, perturbative term and ΔγΔγ is the strongly degenerate elliptic operator of the type

By using a perturbation method introduced by Bolle (J. Differ. Equ. 152:274-288, 1999), we prove the existence of multiple solutions in spite of the lack of symmetry of the problem.