CLASSIFICATION OF POSITIVE SOLUTIONS FOR NONLINEAR DIFFERENTIAL AND INTEGRAL SYSTEMS WITH CRITICAL EXPONENTS

摘要

We classify all positive solutions for the following integral system……Here fi(u), 1≤i≤m, are real-valued functions of homogeneous degree n+α/n-α and aremonotone nondecreasing with respect to all the independent variables u1, u2, ..', um. In the special case n>3 and α= 2, we show that the above system is equivalent to the following elliptic PDE system………This system is closely related to the stationary Schrodinger system with critical exponents for Bose-Einstein condensate.