A Note On The Existence Of Positive Solution For A Class Of Laplacian Nonlinear System With Sign-changing Weight

Abstract

This study concerns the existence of positive solution for the systemwhere λ > 0 is a parameter, Ω is a bounded domain in R N (N > 1) with smooth boundary ∂Ω and ∆ is the Laplacian operator. Here a(x) and b(x) are C 1 sign-changing functions that maybe negative near the boundary and f , g are C 1 nondecresing functions such that Z. Halimi and Z. Mashhadban/ TJMCS Vol .3 No.3 (2011) 339 -345 for every M > 0.We discuss the existence of positive solution when f , g, a(x) and b(x) satisfy certain additional conditions. We use the method of sub-super solutions to establish our results.

Existence results for fractional Fisher-Kolmogoroff steady state problem

“…Many authors are interested in the study of existence results of weak solutions for linear [31], semilinear [15] and nonlinear systems [19]- [24] by using different methods. In [18,20], the subsuper solutions method is used to give necessary conditions for the existence of positive weak solutions.…”