Pimenta, Marcos T. O. [UNESP]Santos, Gelson Conceicao G. dosSantos Junior, Joao R.2023-07-292023-07-292022-12-28Proceedings of the Royal Society of Edinburgh Section A-mathematics. Cambridge: Cambridge Univ Press, 27 p., 2022.0308-2105http://hdl.handle.net/11449/245555In this work, we study a quasilinear elliptic problem involving the 1-Laplacian operator, with a discontinuous, superlinear and subcritical nonlinearity involving the Heaviside function H(middot - beta). Our approach is based on an analysis of the associated p-Laplacian problem, followed by a thorough analysis of the asymptotic behaviour or such solutions as p -> 1(+). We study also the asymptotic behaviour of the solutions, as beta -> 0(+) and we prove that it converges to a solution of the original problem, without the discontinuity in the nonlinearity.27eng1-Laplacian operatorspace of functions of bounded variationdiscontinuous nonlinearitiesArtigo10.1017/prm.2022.86WOS:000904842100001