where Ω ⊂ R N is an open-bounded domain with smooth boundary, s 1 , s 2 ∈ (0, 1), p 1 , p 2 ∈ (1, + ∞), and 𝛼 1 , 𝛼 2 , 𝛽 1 , 𝛽 2 are positive constants. We first discuss the nonexistence of positive classical solutions to system (S). 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 (S), turn to be Hölder continuous. Finally, we apply a well-known Krasnosel'skiı's argument to establish the uniqueness of such positive pair of solutions.
In this article, we study a class of doubly nonlinear parabolic problems involving the fractional p-Laplace operator. For this problem, we discuss existence, uniqueness and regularity of the weak solutions by using the time-discretization method and monotone arguments. For global weak solutions, we also prove stabilization results by using the accretivity of a suitable associated operator. This property is strongly linked to the Picone identity that provides further a weak comparison principle, barrier estimates and uniqueness of the stationary positive weak solution.
For more information see https://ejde.math.txstate.edu/Volumes/2021/09/abstr.html
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