
Minimax Theory and its Applications 07 (2022), No. 1, 159172 Copyright Heldermann Verlag 2022 Equations with sFractional (p,q)Laplacian and Convolution Dumitru Motreanu Dép. de Mathématiques, Université de Perpignan, France motreanu@univperp.fr This paper deals with a Dirichlet problem on a bounded subdomain Ω of the Ndimensional Euclidean space R^{N} for an equation which is doubly nonlocal: it is driven by the (negative) sfractional (p,q)Laplacian for 0 < s < 1 and 1 < q < p< ∞ and has as reaction term a nonlinearity with an incorporated convolution. Such a problem is considered for the first time. Another major feature concerns the correct formulation for the notion of sfractional (p,q)Laplacian. The stated problem is studied through two different approaches: limit process via finite dimensional approximations and subsupersolution in the nonlocal setting. Keywords: Nonlocal Dirichlet problem, weak solution, sfractional (p,q)Laplacian, convolution, finite dimensional approximation, subsupersolution. MSC: 35S15, 47G20, 35J92. [ Fulltextpdf (133 KB)] for subscribers only. 