Periodic solutions of certain third order differential systems with nonlinear dissipation. (English) Zbl 1040.34049

Summary: We present \(n\)-dimensional analogues to some results obtained by Ezeilo and Omari by studying the existence of \(T\)-periodic solutions for certain third-order nonlinear differential systems of the form \[ X'''+ AX''+ G(t, X')+ CX = P(t), \] where the dissipative term \(G\) and forcing term \(P\) are vector-valued functions, and \(A\) and \(C\) are nonsingular constant matrices. We demonstrate in this study that a transition from the scalar to the vector field is by no means trivial.


34C25 Periodic solutions to ordinary differential equations
37L05 General theory of infinite-dimensional dissipative dynamical systems, nonlinear semigroups, evolution equations
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