Nonlinear vector Duffing inclusions with no growth restriction on the orientor field

Nikolaos S. Papageorgiou, Calogero Vetro, Francesca Vetro

DOI: http://dx.doi.org/10.12775/TMNA.2019.041

Abstract


We consider nonlinear multivalued Dirichlet Duffing systems. We do not impose any growth condition on the multivalued perturbation. Using tools from the theory of nonlinear operators of monotone type, we prove existence theorems for the convex and the nonconvex problems. Also we show the existence of extremal trajectories and show that such solutions are $C_0^1(T,\mathbb{R}^N)$-dense in the solution set of the convex problem (strong relaxation theorem).

Keywords


Duffing system; extremal solutions; nonlinear operator of monotone type; strong relaxations

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