Three solutions for forced duffing-type equations with damping term

Abstract

Using the variational principle of Ricceri and a local mountain pass lemma, we study the existence of three distinct solutions for the following resonant Duffing-type equations with damping and perturbed term u″(t)+ αu′(t) + f (t,u(t)) + λg (t,u(t)) = p (t), a.e. t ∈ [ 0,w], u(0) = 0 = u (w) and without perturbed term u″ (t) + αu′(t) + f (t,u(t)) = p(t), a.e. t∈ [ 0,w], u (0) = 0 = u (w). © 2011 Yongkun Li and Tianwei Zhang.