Turkish Journal

of

Mathematics

math@tubitak.gov.tr

# Turkish Journal of Mathematics

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

H. M. SERAG, S. A. KHAFAGY
Mathematics Department, Faculty of Science,
Al-Azhar University, Nasr City
(11884), Cairo-EGYPT
e-mail: serraghm@yahoo.com, elgharieb@hotmail.com.

Abstract: We study the Maximum Principle and existence of positive weak solutions for the n \times n nonlinear elliptic system -DP,pui=\sumj=1naij(x)|uj|p-2uj+fi(x,u1,u2, ... ,un) in W, ui=0,\ i=1,2,. n on \partial W \} where the degenerated p-Laplacian defined as D P,pu=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''.

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

Turk. J. Math., 34, (2010), 59-72.
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Other articles published in the same issue: Turk. J. Math.,vol.34,iss.1.