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