We consider a multivalued nonlinear Duffing system driven by a nonlinear nonhomogeneous differential operator. We prove existence theorems for both the convex and nonconvex problems (according to whether the multivalued perturbation is convex valued or not). Also, we show that the solutions of the nonconvex problem are dense in those of the convex (relaxation theorem). Our work extends the recent one by Kalita–Kowalski [7].
Papageorgiou, N.S., Vetro, C., Vetro, F. (2018). Nonlinear multivalued Duffing systems. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 468(1), 376-390 [10.1016/j.jmaa.2018.08.024].
Nonlinear multivalued Duffing systems
Vetro, Calogero;
2018-01-01
Abstract
We consider a multivalued nonlinear Duffing system driven by a nonlinear nonhomogeneous differential operator. We prove existence theorems for both the convex and nonconvex problems (according to whether the multivalued perturbation is convex valued or not). Also, we show that the solutions of the nonconvex problem are dense in those of the convex (relaxation theorem). Our work extends the recent one by Kalita–Kowalski [7].
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