Abstract
Here, we are concerned with the positive continuous entire solutions of the Wolff-type integral system {u(x)=C1(x)Wβ,γ(v−q)(x),u,v>0 in ℝn,v(x)=C2(x)Wβ,γ(u−p)(x),p,q>0, where n≥1, γ>1, β>0 and βγ≠n. In addition, Ci(x)(i=1,2) are some double bounded functions. When βγ∈(0,n), the Serrin-type condition is critical for existence of positive solutions for some double bounded functions Ci(x) (i=1,2). Such an integral equation system is related to the study of the γ-Laplace system and k-Hessian system with negative exponents. Estimated by the integral of the Wolff type potential, we obtain the asymptotic rates and the integrability of positive solutions, and study whether the radial solutions exist.
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