Equations with s-Fractional (p, q)-Laplacian and Convolution
Keywords:
Nonlocal Dirichlet problem, weak solution, s-fractional (p, q)-Laplacian, convolution, finite dimensional approximation, sub-supersolution.Abstract
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 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.
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