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.File in questo prodotto:
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