A note on the existence of positive solution for a Class of Quasilinear Elliptic System Involving the indefinite weight functions

In this note, we consider the positive solutions to the singular problem 8>>>>>>>>>< >>>>>>>>>: − u1 = a1(x)u 1 2 , in , − u2 = a2(x)u 2 3 , in , ... − un = an(x)u n 1 , in , ui = 0 for 1 i n x 2 @ (1) where is a positive parameter, is a Laplacian operator, i > 0 for i=1,2,..n. The weight functions ai(x) satisfies ai(x) 2 C( ) and ai(x) > ai 0 > 0 for x 2 and 1 i n. and is a bounded domain inRN(N > 1)with smooth oundary@. By using the method of sub-super solutions we prove the existence of positive solutions for each > 0 .

Keywords:

Quasilinear elliptic system , positive solutions. AMS Subject Classification: 35J65