A reversed Herbst inequality is proved as the critical case of the reversed Stein-Weiss inequality, with existence of extremals and qualitative analysis of their Euler-Lagrange system.
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Positive solutions of the Euler-Lagrange system associated with the reversed Stein-Weiss inequality are radially symmetric and increasing about the origin.
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Reversed inequality of the Herbst-type and the related Euler-Lagrange system
A reversed Herbst inequality is proved as the critical case of the reversed Stein-Weiss inequality, with existence of extremals and qualitative analysis of their Euler-Lagrange system.
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Radial symmetry of positive solutions of an integral system associated with the reversed Stein-Weiss inequality
Positive solutions of the Euler-Lagrange system associated with the reversed Stein-Weiss inequality are radially symmetric and increasing about the origin.