Abstract
In this paper, we study the Dirichlet problem for a class of infinitely degenerate elliptic equations with a free perturbation. By using the logarithmic Sobolev inequality, perturbation theorem and Ekeland's variational principle, we obtain the existence of the infinitely many weak solutions and the existence of the nonnegative weak solution. Furthermore, by the methods of iteration and regularity theorems of degenerate elliptic equations, we can also prove the boundedness of the weak solutions and C∞-regularity of the nonnegative weak solution.
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