Existence and uniqueness of the weak solution for aP-Laplacian problem

In this work, we study the existence and uniqueness of weak solutions for a p-Laplacianproblem in RN of the form:-Deltapu + m(x)|u|p-2u = f(x, u(x)), (1)where 1 < p < N, N 3, m 2 C(RN,R), and 0 < m(x) < +1. Here, f : RN × R ! R is a Carathéodory function that is decreasing with respect to the second variable.Compared to previous work, we have replaced the Laplacian with the p-Laplacian.Using Monotone Operator Theory, we establish the existence of a non-trivial solution.In RN, the main difficulty is the lack of compactness. To overcome this, we impose additional assumptions on the nonlinear term f(x, u).

Autorentext

Graduate of the Higher Normal School of Kouba and holder of a doctorate from Amar Telidji University of Laghouat.