A Wolff Type Integral Equations Solution

Many problems in the fields of science, engineering technology and mathematic theory itself mostly come down to solving integral equations, especially nonlinear integral equations. Wolff potential and integral equations of Wolff type play important roles in researches of nonlinear differential (integral) equations.We consider a class of fully nonlinear integral systems of Wolff type: (?)u(x)=Wβ,γ(f(u,v))(x) x∈Rn v(x)=Wβ,γ(g(u,v))(x) x∈Rn wherePositive solution properties of the above systems are researched in this thesis using the method of moving planes in integral forms, homogenous norm estimation and measure classification, etc. A conclusion is deduced that the positive solution pair(u(x),v(x))is radial symmetric and monotone nondecreasing about some point in R ". And this conclusion is further extended to general systems containing m variables and m essentially correlated equations. In addition, some discussions are made about the problems of two-variable systems without essential correlation.