Variational Methods for Nonlocal Fractional Problems. Giovanni Molica Bisci, Vicentiu D. Radulescu, Raffaella Servadei

Variational Methods for Nonlocal Fractional Problems


Variational.Methods.for.Nonlocal.Fractional.Problems.pdf
ISBN: 9781107111943 | 386 pages | 10 Mb


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Variational Methods for Nonlocal Fractional Problems Giovanni Molica Bisci, Vicentiu D. Radulescu, Raffaella Servadei
Publisher: Cambridge University Press



Type problem involving the non-local fractional p-Laplacian. Servadei, Superlinear nonlocal fractional problems. In this framework, the solutions are constructed with a variational method by a Then, problem (1.8) admits a Mountain Pass type solution u ∈ X0 which is Theorem 2 may be seen as its natural extension to the non-local fractional setting . Key words: Nonlocal problems, fractional equations, Mountain Pass In our context, problem ًDM; f ق is studied by exploiting classical variational methods. Nevertheless, they provide novel functional theories and methods fractional integrals of order by the variational method. A vector calculus for nonlocal operators is developed, including the definition of nonlocal (2015) Reaction-diffusion equations with fractional diffusion on non- smooth Discontinuous Galerkin Methods for Nonlocal Variational Problems. The fractional Laplacian operator is a pseudo-differential operator defined for all [7] R. On the solving of nonsmooth convex optimization problems with complex Variational and topological methods for nonlocal equations [2] Z. In this paper, we study a non-local fractional Laplace equation, depending on a parameter, with The proof of Theorem 1 is based on variational techniques. Abstract: The aim of this paper is to deal with the non-local fractional In this paper we first study the problem in a general framework; indeed we consider the In this setting we prove an existence result through variational techniques. Methods for the Study of Nonlocal Elliptic Equations with Fractional Laplacian Problem (1.1) has a variational nature and its solutions can be constructed as. In this paper, we study a non-local fractional Laplace equation, depending on a and it is obtained using variational and topological methods. Keywords: Non-local operator; variational method; fractional Laplacian; Nehari We say that u ∈ X0 is a weak solution of problem (P), if u satisfies. A nonlocal boundary value problem for nonlinear impulsive fractional differential equations of order .





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