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Operator with non standard growth

Grant number: 19/23917-3
Support Opportunities:Regular Research Grants
Duration: February 01, 2020 - October 31, 2021
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Analysis
Principal Investigator:Alessio Fiscella
Grantee:Alessio Fiscella
Host Institution: Instituto de Matemática, Estatística e Computação Científica (IMECC). Universidade Estadual de Campinas (UNICAMP). Campinas , SP, Brazil

Abstract

This research project focuses on the study of nonlinear elliptic problems driven by operators with non standard growth. In particular, in this project we intend to work on the following directions.(1) In the first topic, with Prof. Sitong Chen (Central South University), Prof. Patrizia Pucci (Università degli Studi di Perugia) and Prof. Xianhua Tang (Central South University), we are studying multiplicity results for systems of two equations driven by (p,N) Laplacian and involving critical exponential terms.(2) In the second topic, joint with Prof. Giuseppe Mingione (Università degli Studi di Parma), we will study a Kirchhoff problem with a double phase operator; with Prof. Patrizia Pucci, we will study equations with the same operator but defined in the entire space RN.(3) Joint with Prof. Patrizia Pucci, we will also study a generalization of the (p,q) Laplacian on a fractional framework; with Dr. Jiabin Zhuo (Hohai University), we will solve problems with the fractional p(·)-Laplacian with variable order s(·).(4) Finally, with Prof. Andrea Pinamonti (Università degli Studi di Trento), we are interested in studying the resonant problem with an operator given by the combination of local p-Laplacian and nonlocal fractional p-Laplacian. (AU)

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Scientific publications (8)
(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)
ZUO, JIABIN; FISCELLA, ALESSIO; BAHROUNI, ANOUAR. xistence and multiplicity results for p(.)&q(.) fractional Choquard problems with variable orde. Complex Variables and Elliptic Equations, v. 67, n. 2, . (19/23917-3, 19/02512-5)
FARKAS, CSABA; FISCELLA, ALESSIO; WINKERT, PATRICK. Singular Finsler Double Phase Problems with Nonlinear Boundary Condition. ADVANCED NONLINEAR STUDIES, v. 21, n. 4, p. 809-825, . (19/02512-5, 19/23917-3)
FARKAS, CSABA; FISCELLA, ALESSIO; WINKERT, PATRICK. On a class of critical double phase problems. Journal of Mathematical Analysis and Applications, v. 515, n. 2, p. 16-pg., . (19/23917-3, 19/02512-5)
CHEN, SITONG; FISCELLA, ALESSIO; PUCCI, PATRIZIA; TANG, XIANHUA. Coupled elliptic systems in R-N with (p, N) Laplacian and critical exponential nonlinearities. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, v. 201, p. 14-pg., . (19/02512-5, 19/23917-3)
FISCELLA, ALESSIO. A Double Phase Problem Involving Hardy Potentials. APPLIED MATHEMATICS AND OPTIMIZATION, v. 85, n. 3, p. 16-pg., . (19/23917-3, 19/02512-5)
FISCELLA, ALESSIO; PUCCI, PATRIZIA. DEGENERATE KIRCHHOFF (p,q)-FRACTIONAL SYSTEMS WITH CRITICAL NONLINEARITIES. FRACTIONAL CALCULUS AND APPLIED ANALYSIS, v. 23, n. 3, p. 723-752, . (19/02512-5, 19/23917-3)
ZUO, JIABIN; FISCELLA, ALESSIO; BAHROUNI, ANOUAR. Existence and multiplicity results for p(.)&q(.) fractional Choquard problems with variable order. Complex Variables and Elliptic Equations, v. 67, n. 2, p. 17-pg., . (19/02512-5, 19/23917-3)
FISCELLA, ALESSIO; MISHRA, PAWAN KUMAR. Fractional Kirchhoff Hardy problems with singular and critical Sobolev nonlinearities. MANUSCRIPTA MATHEMATICA, v. 168, n. 1-2, p. 45-pg., . (19/02512-5, 19/23917-3)

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