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2016, Encyclopedia of mathematics and its applications, ISBN 1107111943, Volume 162, xvi, 383 pages
.... 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... 
Calculus | Fractional calculus
Book
Fractional Calculus and Applied Analysis, ISSN 1311-0454, 10/2019, Volume 22, Issue 5, pp. 1351 - 1377
...RESEARCH PAPER SUPERCRITICAL FRACTIONAL KIRCHHOFF TYPE PROBLEMS Vincenzo Ambrosio 1, Raffaella Servadei 2 Abstract In this paper we deal with the following... 
Kirchhoff equation | Primary: 49J35 | 35A15 | critical exponent | fractional | Mountain Pass Theorem | Secondary: 47G20 | 35S15 | 45G05 | Laplacian | MATHEMATICS | fractional p-Laplacian | MATHEMATICS, APPLIED | MATHEMATICS, INTERDISCIPLINARY APPLICATIONS | POSITIVE SOLUTIONS | NONTRIVIAL SOLUTIONS | EQUATIONS | Arrays | Continuity (mathematics) | Parameters
Journal Article
Journal of mathematical analysis and applications, ISSN 0022-247X, 2012, Volume 389, Issue 2, pp. 887 - 898
The purpose of this paper is to study the existence of solutions for equations driven by a non-local integrodifferential operator with homogeneous Dirichlet... 
Mountain Pass Theorem | Fractional Laplacian | Integrodifferential operators | Variational techniques | MATHEMATICS | MATHEMATICS, APPLIED
Journal Article
Discrete and continuous dynamical systems, ISSN 1078-0947, 05/2013, Volume 33, Issue 5, pp. 2105 - 2137
In this paper we study the existence of non-trivial solutions for equations driven by a non-local integrodifferential operator L-K with homogeneous Dirichlet... 
Mountain Pass Theorem | Fractional Laplacian | Integrodifferential operators | Linking Theorem | Variational techniques | MATHEMATICS | MATHEMATICS, APPLIED | variational techniques | fractional Laplacian | integrodifferential operators
Journal Article
manuscripta mathematica, ISSN 0025-2611, 3/2018, Volume 155, Issue 3, pp. 369 - 388
...manuscripta math. 155, 369–388 (2018) © Springer-Verlag GmbH Germany 2017 Alessio Fiscella · Giovanni Molica Bisci · Raffaella Servadei Multiplicity results... 
Geometry | Primary: 49J35 | Topological Groups, Lie Groups | 35A15 | Calculus of Variations and Optimal Control; Optimization | Mathematics, general | Algebraic Geometry | Mathematics | Secondary: 47G20 | Number Theory | 35S15 | 45G05 | MATHEMATICS | EQUATION | BREZIS-NIRENBERG RESULT
Journal Article
Proceedings of the Royal Society of Edinburgh. Section A. Mathematics, ISSN 0308-2105, 08/2014, Volume 144, Issue 4, pp. 831 - 855
In this paper we deal with two non-local operators that are both well known and widely studied in the literature in connection with elliptic problems of... 
MATHEMATICS | MATHEMATICS, APPLIED | LAPLACE EQUATION | REGULARITY | NONLOCAL ELLIPTIC-OPERATORS | EXTENSION PROBLEM | Fractions | Spectrum analysis | Operators | Integrals | Eigenvalues | Projection | Eigenfunctions | Constants | Spectra | Joints
Journal Article
Communications on pure and applied analysis, ISSN 1534-0392, 11/2013, Volume 12, Issue 6, pp. 2445 - 2464
Journal Article
Nonlinear analysis, ISSN 0362-546X, 2019, Volume 189, p. 111561
Journal Article
Advanced Nonlinear Studies, ISSN 1536-1365, 08/2012, Volume 12, Issue 3, pp. 597 - 619
Journal Article
Journal of mathematical analysis and applications, ISSN 0022-247X, 2011, Volume 383, Issue 1, pp. 190 - 199
In this paper we consider a semilinear equation driven by an operator not in divergence form. Precisely, the principal part of the operator is in divergence... 
Critical points theory | Iterative techniques | Variational methods | Semilinear elliptic PDE | Regularity results | EXISTENCE | MATHEMATICS, APPLIED | TERMS | EQUATIONS | GRADIENT | DEPENDENCE | MATHEMATICS | NATURAL GROWTH
Journal Article
Journal of mathematical analysis and applications, ISSN 0022-247X, 08/2017, Volume 452, Issue 2, pp. 883 - 895
This paper concerns with a class of elliptic equations on fractal domains depending on a real parameter. Our approach is based on variational methods. More... 
Sierpiński gasket | Weak Laplacian | Fractal domains | Nonlinear elliptic equation | MATHEMATICS | FRACTALS | MATHEMATICS, APPLIED | MULTIPLE SOLUTIONS | THEOREM | DIRICHLET PROBLEM | Sierpinski gasket | ELLIPTIC-EQUATIONS
Journal Article
Asymptotic analysis, ISSN 0921-7134, 09/2015, Volume 94, Issue 3-4, pp. 347 - 361
In this paper we study a highly nonlocal problem involving a fractional operator combined with a Kirchhoff-type coefficient. The latter is allowed to vanish at... 
variational methods | Krasnoselskii's genus | nonlocal problems | Kirchhoff-type equations | critical point theory | fractional Laplacian | EXISTENCE | MATHEMATICS, APPLIED | BREZIS-NIRENBERG RESULT | VARIATIONAL-METHODS | LAPLACIAN | R-N | DIFFUSION | OPERATORS
Journal Article
Bulletin des sciences mathématiques, ISSN 0007-4497, 02/2016, Volume 140, Issue 1, pp. 14 - 35
In this paper we consider the following critical nonlocal problem{−LKu=λu+|u|2⁎−2uin Ωu=0in Rn∖Ω, where s∈(0,1), Ω is an open bounded subset of Rn, n>2s, with... 
Critical nonlinearities | Fractional Laplacian | Integrodifferential operators | Variational techniques | Best fractional critical Sobolev constant | Secondary | Primary | MATHEMATICS, APPLIED | BREZIS-NIRENBERG RESULT | LOW DIMENSION | ELLIPTIC-EQUATIONS | CRITICAL SOBOLEV EXPONENT | OPERATORS | FUNCTIONALS
Journal Article
Forum Mathematicum, ISSN 0933-7741, 11/2016, Volume 28, Issue 6, pp. 1095 - 1110
We study the question of the existence of infinitely many weak solutions for nonlocal equations of fractional Laplacian type with homogeneous Dirichlet... 
variational methods | superlinear nonlinearities | 49J35 | Fountain theorem | nonlocal problems | 35A15 | 47G20 | integrodifferential operators | Fractional Laplacian | 35S15 | 45G05 | MATHEMATICS | MATHEMATICS, APPLIED | BREZIS-NIRENBERG RESULT | EQUATIONS | Laplace equation | Dirichlet problem | Mathematical analysis | Existence theorems
Journal Article
Nonlinear analysis, ISSN 0362-546X, 2010, Volume 72, Issue 11, pp. 4347 - 4359
Journal Article
Nonlinear analysis, ISSN 0362-546X, 2011, Volume 74, Issue 15, pp. 5161 - 5170
In this work we give a result concerning the continuous dependence on the data for weak solutions of a class of semilinear elliptic variational inequalities (... 
Semilinear elliptic variational inequalities | Stability result | Critical point theory | Penalization method | Variational methods | Gradient-dependent nonlinearity | Iterative techniques | MATHEMATICS | MATHEMATICS, APPLIED | GROWTH | DEPENDENCE | Nonlinearity | Stability | Images | Inequalities | Constraining | Convergence
Journal Article
Discrete and continuous dynamical systems. Series S, ISSN 1937-1632, 08/2012, Volume 5, Issue 4, pp. 819 - 830
The aim of this paper is to use a variational approach in order to obtain the existence of non-trivial weak solutions of a quasilinear elliptic equation not in... 
Critical points theory | Quasilinear elliptic equations | Iterative techniques | Variational methods | Regularity results | variational methods | critical points theory | MATHEMATICS, APPLIED | regularity results | EXISTENCE THEOREMS | GRADIENT | iterative techniques
Journal Article
Nonlinear Differential Equations and Applications NoDEA, ISSN 1021-9722, 11/2006, Volume 13, Issue 3, pp. 311 - 335
Journal Article
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