On maximum principle and existence of positive weak solutions for n\times n nonlinear elliptic systems involving degenerated p-Laplacian operators

Authors

H. M. SERAG
S. A. KHAFAGY

DOI

10.3906/mat-0707-8

Abstract

We study the Maximum Principle and existence of positive weak solutions for the n \times n nonlinear elliptic system -\Delta_{P,p}u_i=\sum_{j=1}^na_{ij}(x) u_j ^{p-2}u_j+f_i(x,u_1,u_2, ... ,u_n) in \Omega, u_i=0,\ i=1,2,. n on \partial \Omega \} where the degenerated p-Laplacian defined as \Delta _{P,p}u=div [P(x) \nabla u ^{p-2}\nabla u] with p>1,p \neq 2 and P(x) is a weight function. We give some conditions for having the Maximum Principle for this system and then we prove the existence of positive weak solutions for the quasilinear system by using ``sub-super solutions method''.

Keywords

Maximum principle, existence of positive weak solution, nonlinear elliptic system, degenerated p-Laplacian.

First Page

59

Last Page

72

Recommended Citation

SERAG, H. M. and KHAFAGY, S. A. (2010) "On maximum principle and existence of positive weak solutions for n\times n nonlinear elliptic systems involving degenerated p-Laplacian operators," Turkish Journal of Mathematics: Vol. 34: No. 1, Article 6. https://doi.org/10.3906/mat-0707-8
Available at: https://journals.tubitak.gov.tr/math/vol34/iss1/6