Nonlinear multivalued Duffing systems

TL;DR

This paper studies multivalued nonlinear Duffing systems driven by complex differential operators, proving existence of solutions for convex and nonconvex cases, and demonstrating the density of nonconvex solutions in convex ones.

Contribution

It extends previous work by establishing existence theorems for both convex and nonconvex multivalued Duffing systems and proving a relaxation theorem about solution density.

Findings

Existence theorems for convex and nonconvex problems

Solutions of nonconvex problems are dense in convex solutions

Extension of previous results by Kalita-Kowalski

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).