LIOUVILLE TYPE THEOREM FOR NONLINEAR ELLIPTIC EQUATION WITH GENERAL NONLINERARITY

In this paper, we study the nonexistence of positive solutions for the following elliptic equation {-Delta u = f(u) in R-+(N,) partial derivative u/partial derivative v - g(u) on partial derivative R-+(N) and elliptic system {-Delta u(1) = f1(u(1),v(1)) in R-+(N) , -Delta u(2) = f(2)(u(2),v(2)) in R-+(N,) partial derivative u(1)/partial derivative v = g(1) (v(1), v(2)) on R-+(N) We will prove that these problems possess no positive solutions under some assumptions on nonlinear terms. The main technique we use is the moving plane method in an integral form.