IJPAM: Volume 107, No. 2 (2016)

EXISTENCE AND UNIQUENESS OF WEAK SOLUTION OF
A NONLINEAR NEUMANN PROBLEM

Bassam Al-Hamzah$^1$, Naji Yebari$^2$
$^{1,2}$Department of Mathematics
Faculty of Sciences
University Abdelmalek Essaadi
Tetouan, MOROCCO


Abstract. This paper deals with the equation

\begin{displaymath}-\Delta_{p} u+a(x)\vert u\vert^{p-2}u= f(x,u)\end{displaymath}

in bounded domain $\Omega \in \mathbb{R}^{N}.$ Relying on Browder theorem, under conditions of the monotonous function $f$. We obtained the existence and uniqueness of weak solutions for the weighted p-laplacian boundary value of the form

\begin{displaymath}
\left\{%
\begin{split}
&-\Delta_{p} u+a(x)\vert u\vert^{p...
...qquad\mbox{on}\ \partial\Omega
\end{split}
\right.\leqno{(P)}\end{displaymath}

in bounded domain $\Omega\in\mathbb{R}^{N}$.

Received: January 4, 2016

AMS Subject Classification:

Key Words and Phrases: weak solutions, p-Laplacian operator, Neumann problem

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DOI: 10.12732/ijpam.v107i2.10 How to cite this paper?

Source:
International Journal of Pure and Applied Mathematics
ISSN printed version: 1311-8080
ISSN on-line version: 1314-3395
Year: 2016
Volume: 107
Issue: 2
Pages: 407 - 414


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