In this paper we study the existence and multiplicity of solutions for a second order nonautonumous periodic system with a nonsmooth potential. We prove two existence theorems and a multiplicity result. In the first existence theorem the Euler functional is coercive and the solution is a minimizer of it. In the second existence theorem the Euler functional is unbounded and the solution is obtained using the saddle point theorem. Finally for the multiplicity result we employ a nonsmooth version of the local linking theorem.

Nonautonomous second order periodic systems: existence and multiplicity of solutions

BARLETTA, Giuseppina;
2007-01-01

Abstract

In this paper we study the existence and multiplicity of solutions for a second order nonautonumous periodic system with a nonsmooth potential. We prove two existence theorems and a multiplicity result. In the first existence theorem the Euler functional is coercive and the solution is a minimizer of it. In the second existence theorem the Euler functional is unbounded and the solution is obtained using the saddle point theorem. Finally for the multiplicity result we employ a nonsmooth version of the local linking theorem.
2007
Nonsmooth potential; Locally Lipschitz function; Multiple nontrivial solutions
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/20.500.12318/839
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