Three Solutions for Forced Duffing-Type Equations with Damping Term

Correspondence should be addressed to Yongkun Li, [email protected] Received 16 December 2010; Revised 6 February 2011; Accepted 11 February 2011 Academic Editor: Dumitru Motreanu Copyright q 2011 Y. Li and T. Zhang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. 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 σu′ t f t, u t λg t, u t p t , a.e. t ∈ 0, ω , u 0 0 u ω and without perturbed term u′′ t σu′ t f t, u t p t , a.e. t ∈ 0, ω , u 0 0 u ω .