Geodesic
Equations with \(s\)-fractional \((p,q)\)-Laplacian and convolution
Minimax theory and its applications, Tome 7 (2022) no. 1
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This paper deals with a Dirichlet problem on a bounded domain Ω ⊂ R N for an equation which is doubly nonlocal: it is driven by the (negative) s-fractional (p, q)-Laplacian for s ∈ (0, 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 notionof 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.
Mots-clés : Nonlocal Dirichlet problem, weak solution, s-fractional (p, q)-Laplacian, convolution, finite dimensional approximation, sub-supersolution 
@article{MTA_2022_7_1_a6,
     author = {Dumitru Motreanu},
     title = {Equations with \(s\)-fractional {\((p,q)\)-Laplacian} and convolution},
     journal = {Minimax theory and its applications},
     year = {2022},
     volume = {7},
     number = {1},
     zbl = {1487.35467},
     url = {http://geodesic.mathdoc.fr/item/MTA_2022_7_1_a6/}
}
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Dumitru Motreanu. Equations with \(s\)-fractional \((p,q)\)-Laplacian and convolution. Minimax theory and its applications, Tome 7 (2022) no. 1. http://geodesic.mathdoc.fr/item/MTA_2022_7_1_a6/