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

By Khaldi Oussama

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

By Khaldi Oussama

0 - Default Title
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 < 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).
Product details
Binding:
Paperback
Number of Pages:
52
Release Date:
2025-06-24
Publication Date:
2025-06-24
Publisher:
LAP LAMBERT Academic Publishing
Languages:
Original: English
ISBN10:
6206685969
ISBN13:
9786206685968
GPSR Manufacturer Reference:
[email protected]
Weight:
96 g
Height:
150 cm
Width:
220 cm
Thickness:
4 cm
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