Research Grants 17/19752-3 - Equações diferenciais parciais, Métodos variacionais - BV FAPESP
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Fractional problems with lack of compactness

Abstract

This research project focuses on the study of nonlinear elliptic problems driven by nonlocal fractional operators with lack of compactness. In particular, in this project we intend to work on the following directions.(1) In the first topic, with Prof. Patrizia Pucci (Università degli Studi di Perugia) and Prof. Binlin Zhang (HeilongjiangInstitute of Technology) we will study existence results for fractional systems involving critical terms.(2) In the second topic, joint with Dr. Vincenzo Ambrosio (Università degli Studi Urbino "Carlo Bo") we will study multiplicity results for fractional problems involving a critical Sobolev term and a Hardy potential.(3) Joint with Dr. Pawan Mishra (Universidade Federal da Paraíba), we will try to study fractional Kirchhoff type problems involving a Sobolev term and a singular one.(4) Finally, with Prof. Andrea Pinamonti (Università degli Studi di Trento) and Dr. Eugenio Vecchi (Università degli Studi di Bologna) we want to extend some classical existence and multiplicity results, proved for the Laplacian and the fractional Laplacian, to the complex case of the fractional magnetic Laplacian. (AU)

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Scientific publications (18)
(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)
FISCELLA, ALESSIO. Multiple Entire Solutions for Schrodinger-Hardy Systems Involving Two Fractional Operators. MINIMAX THEORY AND ITS APPLICATIONS, v. 4, n. 1, SI, p. 101-112, . (17/19752-3)
AMBROSIO, VINCENZO; FISCELLA, ALESSIO; ISERNIA, TERESA. Infinitely many solutions for fractional Kirchhoff-Sobolev-Hardy critical problems. Electronic Journal of Qualitative Theory of Differential Equations, n. 25, p. 1-13, . (17/19752-3)
FISCELLA, ALESSIO; MISHRA, PAWAN KUMAR. The Nehari manifold for fractional Kirchhoff problems involving singular and critical terms. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v. 186, n. SI, p. 6-32, . (17/19752-3)
FISCELLA, ALESSIO; PUCCI, PATRIZIA. (p, N) equations with critical exponential nonlinearities in R-N. Journal of Mathematical Analysis and Applications, v. 501, n. 1, SI, . (17/19752-3)
FISCELLA, ALESSIO; PUCCI, PATRIZIA; ZHANG, BINLIN. p-fractional Hardy-Schrodinger-Kirchhoff systems with critical nonlinearities. ADVANCES IN NONLINEAR ANALYSIS, v. 8, n. 1, p. 1111-1131, . (17/19752-3)
FISCELLA, ALESSIO; PUCCI, PATRIZIA. (p, q) systems with critical terms in R-N. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v. 177, p. 26-pg., . (17/19752-3)
FISCELLA, ALESSIO; VECCHI, EUGENIO. BIFURCATION AND MULTIPLICITY RESULTS FOR CRITICAL MAGNETIC FRACTIONAL PROBLEMS. Electronic Journal of Differential Equations, v. N/A, p. 18-pg., . (17/19752-3)
FISCELLA, ALESSIO; PUCCI, PATRIZIA. (p, q) systems with critical terms in R-N. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v. 177, n. B, p. 454-479, . (17/19752-3)
FISCELLA, ALESSIO; VECCHI, EUGENIO. BIFURCATION AND MULTIPLICITY RESULTS FOR CRITICAL MAGNETIC FRACTIONAL PROBLEMS. Electronic Journal of Differential Equations, . (17/19752-3)
FISCELLA, ALESSIO. SCHRODINGER-KIRCHHOFF-HARDY p-RACTIONAL EQUATIONS WITHOUT THE AMBROSETTI-RABINOWITZ CONDITION. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, v. 13, n. 7, SI, p. 1993-2007, . (17/19752-3)
ZUO, JIABIN; AN, TIANQING; FISCELLA, ALESSIO. A critical Kirchhoff-type problem driven by a p (.)-fractional Laplace operator with variable s (.) -order. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, v. 44, n. 1, p. 1071-1085, . (17/19752-3, 19/02512-5)
FISCELLA, ALESSIO; MIRZAEE, HADI. Fractional p-Laplacian Problems with Hardy Terms and Critical Exponents. ZEITSCHRIFT FUR ANALYSIS UND IHRE ANWENDUNGEN, v. 38, n. 4, p. 483-498, . (17/19752-3)
FISCELLA, ALESSIO; PUCCI, PATRIZIA. (p, N) equations with critical exponential nonlinearities in R-N. Journal of Mathematical Analysis and Applications, v. 501, n. 1, p. 25-pg., . (17/19752-3)
FISCELLA, ALESSIO. Multiple Entire Solutions for Schrodinger-Hardy Systems Involving Two Fractional Operators. MINIMAX THEORY AND ITS APPLICATIONS, v. 4, n. 1, p. 12-pg., . (17/19752-3)
AMBROSIO, VINCENZO; FISCELLA, ALESSIO; ISERNIA, TERESA. Infinitely many solutions for fractional Kirchhoff-Sobolev-Hardy critical problems. Electronic Journal of Qualitative Theory of Differential Equations, v. N/A, n. 25, p. 13-pg., . (17/19752-3)
FISCELLA, ALESSIO; MISHRA, PAWAN KUMAR. The Nehari manifold for fractional Kirchhoff problems involving singular and critical terms. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v. 186, p. 27-pg., . (17/19752-3)
FISCELLA, ALESSIO. SCHRODINGER-KIRCHHOFF-HARDY p-RACTIONAL EQUATIONS WITHOUT THE AMBROSETTI-RABINOWITZ CONDITION. DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS-SERIES S, v. 13, n. 7, p. 15-pg., . (17/19752-3)
ZUO, JIABIN; AN, TIANQING; FISCELLA, ALESSIO. A critical Kirchhoff-type problem driven by a p(.)-fractional Laplace operator with variable s(.)-order. MATHEMATICAL METHODS IN THE APPLIED SCIENCES, v. 44, n. 1, . (17/19752-3, 19/02512-5)

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