## Variational Methods for Nonlocal Fractional Problems by Giovanni Molica Bisci, Vicentiu D. Radulescu, Raffaella Servadei  • Variational Methods for Nonlocal Fractional Problems
• Page: 386
• Format: pdf, ePub, mobi, fb2
• ISBN: 9781107111943
• Publisher: Cambridge University Press

This book provides researchers and graduate students with a thorough introduction to the variational analysis of nonlinear problems described by nonlocal operators. The authors give a systematic treatment of the basic mathematical theory and constructive methods for these classes of nonlinear equations, plus their application to various processes arising in the applied sciences. The equations are examined from several viewpoints, with the calculus of variations as the unifying theme. Part I begins the book with some basic facts about fractional Sobolev spaces. Part II is dedicated to the analysis of fractional elliptic problems involving subcritical nonlinearities, via classical variational methods and other novel approaches. Finally, Part III contains a selection of recent results on critical fractional equations. A careful balance is struck between rigorous mathematics and physical applications, allowing readers to see how these diverse topics relate to other important areas, including topology, functional analysis, mathematical physics, and potential theory.

Mountain Pass solutions for non-local elliptic operators
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 . Differential and integral equations, dynamical systems and control
Variational Methods for Nonlocal Fractional Problems. Molica Bisci Multiscale Methods for Fredholm Integral Equations. Chen, Zhongying Fractional $p$-eigenvalues - Calculus of Variations and Geometric
class of nonlocal operators whose model is the fractional p-Laplacian. Keywords. Nonlinear eigenvalues problems, nonlocal problem, frac- tional Laplacian [22 ] R. Servadei, E. Valdinoci: Variational methods for non-local operators of. Superlinear nonlocal fractional problems with infinitely - IOPscience
nonlocal fractional problems are widely studied in the literature in  Ambrosetti A and Rabinowitz P 1973 Dual variational methods in  Variational Methods for Nonlocal Fractional Problems - Cambridge
Variational Methods for Nonlocal Fractional Problems. Series: Encyclopedia of Mathematics and its Applications (No. 162). Giovanni Molica Bisci. Università di  Existence of two solutions for a second-order discrete boundary
Similar variational methods can be used to study various problems, see for Article: Multiplicity of solutions for a class of superlinear non-local fractional  Variational Methods for Nonlocal Fractional Problems - BookManager
Title: Variational Methods for Nonlocal Fractional Problems Author: Bisci, Giovanni Radulescu, Vicentiu Servadei, Raffaella  Non-local boundary value problems for impulsive fractional integro
boundary value problem Caputo type fractional derivative existence and uniqueness fixed point theorem impulsive integro-differential equation nonlocal  View paper
stant, variational techniques, integrodifferential operators. interesting existence results for nonlocal problems driven by fractional operators in a critical. On four-point nonlocal boundary value problems of nonlinear
On four-point nonlocal boundary value problems of nonlinear integro-differential system of nonlinear fractional differential equations via variational methods. GNAMPA Project 2014 (R. Bartolo, A. Fiscella, G. Molica Bisci, R
A. Fiscella, Variational problems involving nonlocal fractional operators, R. Servadei, Variational methods for nonlocal equations, Università degli Studi di  Stationary Kirchhoff problems involving a fractional elliptic operator
The main nonlocal fractional operator LK is defined for any x ∈ Rn by variational methods, while in  the authors extend the theorems got  AIMS Home
Variational methods for non-local operators of elliptic type More precisely, we consider the problem \left\{ \begin{array}{ll} \mathcal L_K u+\lambda u+f(x Theorem, variational techniques, integrodifferential operators, fractional Laplacian. Get PDF
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.

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