Decay Rates for Solutions of an Integral System of Wolff Type

作者：Lei Yutian^*

来源：Potential Analysis, 2011, 35(4): 387-402.

DOI：10.1007/s11118-010-9218-5

• Integral equations
• Wolff potential
• Decay rate
• Asymptotic analysis

In this paper, we study the asymptotic behavior of the positive solutions of the following system of involving Wolff potentials in R(n)
u(x) = W(beta,gamma) (v(q)) (x),
v(x) = W(beta,gamma) (u(p)) (x).
Applying the integrability intervals of u and v which were established recently by Chen et al., we obtain the decay rates of the solutions near infinity. In the special case of gamma = 2 and beta = alpha/2, the Wolff type system becomes an integral system of Hardy-Littlewood-Sobolev type. Thus, we also establish the decay rates of the positive solutions of the Hardy-Littlewood-Sobolev type integral system.

• 出版日期2011-11
• 单位南京师范大学