PRIN2017

Nonlinear Differential Problems via Variational, Topological and Set-valued Methods

codice: 2017AYM8XW

Action line: C sud         Main ERC field: PE – Physical Sciences and Engineering

 

Principal Investigator: Gabriele Bonanno, University of Messina

Associated Investigator: Antonio Iannizzotto, University of Cagliari

Associated Investigator: Salvatore Angelo Marano, University of Catania

Associated Investigator: Annamaria Barbagallo, University of Naples “Federico II”

Associated Investigator: Roberto Livrea, University of Palermo

Associated Investigator: Pasquale Candito, University of Reggio Calabria

 

The main aim of the present research project is to investigate nonlinear differential problems in order to obtain general laws on the nonlinearity which guarantee the existence or the multiplicity of solutions.
The principal methods that will be used are variational techniques as well as topological tools and set-valued functions arguments. More precisely, nonlinear ordinary differential equations with different types of boundary values and nonlinear elliptic differential equations with appropriate boundary conditions to obtain the existence of one, two, three, infinitely many solutions will be examined. Elliptic operators with variable exponent, or fractional type operator as well as the discrete or impulsive cases will also be studied. Furthermore, problems in unbounded domains and those with critical growth will also be considered by using a novel condition of weak Palais Smale type. Finally, among the possible applications of previous results, the study of equilibrium problems in economics field by using variational inequalities
will be approched.