Variational Methods for Nonlocal Fractional Problems

By Giovanni Molica Bisci, Vicentiu D. Rădulescu, Raffaella Servadei. 2016

768 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/391cf84a827300f83eef3815ad3b61687c95c7e7

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In Applied Mathematics

In Computational Theory and Mathematics

In Numerical Analysis

Citations in the corpus

On a new fractional Sobolev space and applications to nonlocal variational problems with variable exponent (2017, methodology): “We also refer to the recent monographs [15, 5, 10] for a thorough variational approach of nonlocal problems.”
Weyl and Marchaud Derivatives: A Forgotten History (2017, background): “For further insights to the properties of the fractional Laplace operator, in addition to [3,38,44,45,53,54], we point out also the very recent preprint [55].”
Existence of solutions for perturbed fractional p-Laplacian equations (2016, background): “For the basic properties of fractional Sobolev spaces with applications to partially differential equations, we refer the reader to [15,24] and the references therein.”
p-fractional Hardy–Schrödinger–Kirchhoff systems with critical nonlinearities (2018, methodology): “For critical equations in RN we refer the reader to [2, 7, 11, 14, 29] and references therein for the study of scalar problems with critical nonlinearities.”
On Dirichlet problem for fractional p-Laplacian with singular non-linearity (2016, background): “For detailed study and recent results on this subject, we refer to [35].”
Kirchhoff–Hardy Fractional Problems with Lack of Compactness (2017, background): “These models arise in a quite natural way in many different applications, and we refer to the recent monograph [27], to the extensive paper [10] and the references cited therein for further details.”
Basic results of fractional Orlicz-Sobolev space and applications to non-local problems (2019, background): “rs were written on problems involving the fractional diﬀusion operator (−∆)s (0 < s < 1). We can quote [4, 15, 28, 30, 35, 36] and the references therein. We also refer to the recent monographs [15, 29] for a thorough variational approach of non-local problems. On the other hand, for some nonh”
Combined effects in mixed local–nonlocal stationary problems (2021, background): “Some questions related to structural results like existence, maximum principle and interior Sobolev and Lipschitz regularity [1, 11, 14], symmetry results [13], Faber-Krahn type inequality [12], Neumann problems [42], Green functions estimates [26, 27] has been answered.”