The Existence Of Positiye Solution For Some Nonlinear Elliptic Equations

In this paper, we investigate the existence and stability of positive solutions for some nonlinear elliptic problems.In chapter 1, we study the symmetry of components of positive solutions for γ-Laplacian system where △γu= div(|â–½u|γ-2â–½u) with 1<γ< n, f, g:[0,+∞)â†'R is continuous satisfying the ’monotonicity’ assumptionIn chapter 2, we investigate the stability of solution for Schrodinger - Possion system where n≥ 3, p> 1, and we also give the Joseph-Lundgren(JL) exponent, which is important for the existence of stable solution.In chapter 3, we investigate the existence of positive stable solution and the sta-bility of singular solution for the fully nonlinear elliptic equation-k-Hessian equation with radial structure, where n≥3,1< k< n/2 and p> 1. Moreover, we obtain the JL exponent.