Nonlinear multivalued Duffing systems

2018/04/30 by Nikolaos S. Papageorgiou, Calogero Vetro, Papageorgiou, Nikolaos S. +3
Mathematics · #Advanced Differential Equations and Dynamical Systems #Fractional Differential Equations Solutions #Nonlinear Differential Equations Analysis #math.AP #math.CA #msc:34A60 #msc:34B15

paper · pdf · doi:10.48550/arxiv.1804.11070

arxiv created 2018/04/30 · arxiv updated 2018/05/01

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 (JMAA, https://doi.org/10.1016/j.jmaa. 2018.01.067).

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