The Existence Of Positive Solutions Of A Semiliner Elliptic Equation With A Nonlinear Boundary Condition

The article introduces the multiple existence of positive solutions of a semi-linear elliptic equation in R+n with a nonlinear boundary condition: in which f and g satisfy some conditions, a and b arc radical symmetric and decreas-ing with respect to|x|outside of a bounded domain,and satisfy some condition in a bounded domain, n>2, x’=(x1;x2,…,xn-1). we build a eigenvalue prob-lem in the half ball to approximate the question and get our result through the potential theory and the moving plane method.