Turkish Journal of MathematicsOn maximum principle and existence of positive weak solutions for n\times n nonlinear elliptic systems involving degenerated p-Laplacian operators
Mathematics Department, Faculty of Science,
Al-Azhar University, Nasr City
e-mail: email@example.com, firstname.lastname@example.org.
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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