Multiplicity Results for some Quasilinear Differential Systems with Periodic Nonlinearities
Keywords:
Periodic solutions, periodic nonlinearities, relativistic pendulum systems.Abstract
A multiplicity result for periodic problems of the form −(ψ(u′))′ = ∇uV(t,u)+e(t), u(0) = u(T), u′(0) = u′(T), when ψ : RN → RN belongs to a suitable class of homeomorphisms, V is Ti-periodic in each component ui of u ∈ RN, and e has mean value zero on [0,T] is proved, and applied, by a modification technique, to obtain the same multiplicity for the solutions of the relativistic system
′ − u′ 1 −|u′|2 =∇uV(t,u)+e(t), u(0) = u(T), u′(0) = u′(T)
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