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 $C_0^1(T,IR^N)$-dense in the solution set of the convex problem (strong relaxation theorem)
Papageorgiou N.S., Vetro C., Vetro F. (2019). Nonlinear vector duffing inclusions with no growth restriction on the orientor field. TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS, 54(1), 257-274 [10.12775/TMNA.2019.041].
Nonlinear vector duffing inclusions with no growth restriction on the orientor field
Vetro C.;
2019-01-01
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 $C_0^1(T,IR^N)$-dense in the solution set of the convex problem (strong relaxation theorem)
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