Nontrivial solutions for superquadratic nonautonomous periodic systems

Shouchuan Hu, Nikolaos S. Papageorgiou

DOI: http://dx.doi.org/10.12775/TMNA.2009.045

Abstract


We consider a nonautonomous second order periodic system with an
indefinite linear part. We assume that the potential function is
superquadratic, but it may not satisfy the Ambrosetti-Rabinowitz
condition. Using an existence result for $C^1$-functionals
having a local linking at the origin, we show that the system has
at least one nontrivial solution.

Keywords


Superquadratic potential; AR-condition; spectral resolution; local linking; C-condition; periodic solution

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