{"product_id":"khaldi-oussama-existence-and-uniqueness-of-the-weak-solution-for-ap-laplacian-problem-9786206685968","title":"Existence and uniqueness of the weak solution for aP-Laplacian problem","description":"In this work, we study the existence and uniqueness of weak solutions for a p-Laplacianproblem in RN of the form:¿¿pu + m(x)|u|p¿2u = f(x, u(x)), (1)where 1 \u0026lt; p \u0026lt; N, N 3, m 2 C(RN,R), and 0 \u0026lt; m(x) \u0026lt; +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).","brand":"LAP LAMBERT Academic Publishing","offers":[{"title":"Default Title","offer_id":53722264830294,"sku":null,"price":0.0,"currency_code":"EUR","in_stock":false}],"url":"https:\/\/www.momoxbooks.com\/products\/khaldi-oussama-existence-and-uniqueness-of-the-weak-solution-for-ap-laplacian-problem-9786206685968","provider":"momoxbooks","version":"1.0","type":"link"}