Upper And Lower Solutions Methods And Its Application

In this paper, we consider the upper and lower solutions theorem and the existence of solutions for the following nonlinear elliptic equation in unbounded domains.-div(a(x)▽u)= f(x,u), x∈RN Where a(x)∈C1(RN), a(x)>0, N(?)3,0<α<1. The existence of in-finitely many positive entire solutions for above problem is obtained under some assumptions on u(x) and f(x,u). Moreover, by using the upper and lower solu-tions methods, we have proved that the existence of a positive solution for the following elliptic systems WhereΩis bounded domain in RN with smooth boundary (?)Ω, p>1,μ(?)0, f∈C1,g∈C1.