Abstract

In this paper, we are concerned with the positive solutions of the Wolfftype integral system

where n ≥ 1, γ > 1, β > 0, βγ ̸= n and C_i(x) (i = 1, · · ·, m) are double bounded functions. Discussed in three situations of the integral system, a special iteration scheme in integral form as well as in differential form are applied. By some critical asymptotic analysis with Wolff potential integral estimates, we study the existence and nonexistence of the positive solutions, especially the radial solutions. Furthermore we obtain the asymptotic rates and the integrability of positive solutions.

中文翻译：

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包含 m 个方程的 Wolff 型积分系统

摘要

在本文中，我们关注 Wolff 型积分系统的正解

其中n ≥ 1 , γ > 1 , β > 0, βγ ̸ = n和C _i ( x ) ( i = 1 , · · ·, m ) 是双界函数。讨论了积分系统的三种情况，应用了一种特殊的积分形式和微分形式的迭代方案。通过一些带有 Wolff 势积分估计的关键渐近分析，我们研究了正解的存在和不存在，尤其是径向解。此外，我们获得了渐近率和正解的可积性。