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Minimax Theory and its Applications 07 (2022), No. 1, 159--172
Copyright Heldermann Verlag 2022

Equations with s-Fractional (p,q)-Laplacian and Convolution

Dumitru Motreanu
Dép. de Mathématiques, Université de Perpignan, France

This paper deals with a Dirichlet problem on a bounded subdomain Ω of the N-dimensional Euclidean space RN for an equation which is doubly nonlocal: it is driven by the (negative) s-fractional (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 s-fractional (p,q)-Laplacian. The stated problem is studied through two different approaches: limit process via finite dimensional approximations and sub-supersolution in the nonlocal setting.

Keywords: Nonlocal Dirichlet problem, weak solution, s-fractional (p,q)-Laplacian, convolution, finite dimensional approximation, sub-supersolution.

MSC: 35S15, 47G20, 35J92.

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