Mathematical analysis proves existence of solutions to first- and second-order fractional p-Laplacian evolution equations without monotonicity, highlighting new Galerkin methods for nonlocal...
In this work, existence results on nonlinear first order as well as doubly nonlinear second-order evolution equations involving the fractional |p|-Laplacian are presented. The proofs do not exploit any monotonicity assumption but rely on a compactness argument in combination with regularity of the Galerkin scheme and the nonlocal character of the operator.
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Dimitri Puhst (2015) studied this question.
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