Nonlinear fractional and singular systems: Nonexistence, existence, uniqueness, and Hölder regularity

Abstract

In the present paper, we investigate the following singular quasilinear elliptic system: where is an open‐bounded domain with smooth boundary, s1, s2 ∈ (0, 1), p1, p2 ∈ (1, + ∞), and α1, α2, β1, β2 are positive constants. We first discuss the nonexistence of positive classical solutions to system . Next, constructing suitable ordered pairs of subsolutions and supersolutions, we apply Schauder's fixed‐point theorem in the associated conical shell and get the existence of a positive weak solutions pair to , turn to be Hölder continuous. Finally, we apply a well‐known Krasnosel'skiı̆'s argument to establish the uniqueness of such positive pair of solutions.