Multiple Sign-Changing Solutions for Quasilinear Equations of Bounded Quasilinearity

Abstract

The existence of an infinite sequence of sign-changing solutions are proved for a class of quasilinear elliptic equations under suitable conditions on the quasilinear coefficients and the nonlinearity

where $\Omega\subset\mathbb{R}^N$ is a bounded domain with smooth boundary, and we use

The main interest of this paper is for the case of bounded quasilinearity $b_{ij}$. The result is proved by an elliptic regularization method involving truncations of both $u$ and the gradient of $u$.