On a quasilinear elliptic problem involving the 1-Laplacian operator and a discontinuous nonlinearity

In this work, we study a quasilinear elliptic problem involving the 1-Laplacian operator, with discontinuous, superlinear and subcritical nonlinearity Heaviside function $H(\cdot - \beta )$ . Our approach is based on an analysis of associated p-Laplacian problem, followed by thorough asymptotic behaviour or such solutions as $p \to 1^+$ We also solutions, $\beta 0^+$ prove that it converges to solution original without discontinuity in nonlinearity.