Existence and uniqueness of the weak solution for aP-Laplacian problem
Existence and uniqueness of the weak solution for a P-Laplacian problem in RN
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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 t...
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).
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