Operator with non standard growth

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)