The Existence and Uniqueness of Solution of Duffing Equations with Non-C2 Perturbation Functional at Nonresonance

In recent years, many authors are greatly attached to investigation for the existence and uniqueness of solution of Duffing equations, for example, 1–11 , and so forth. Some authors 8, 11, 12 , etc. proved the existence and uniqueness of solution of Duffing equations underC2 perturbation functions and other conditions at nonresonance by employingminimax theorems. In 1986, Tersian investigated the equation u′′ f t, u t −p t using a minimax theorem proved by himself and reaped a result of generalized solution 13 . In 2005, Huang and Shen generalized the minimax theorem of Tersian in 13 . Using the generalized minimax theorem, Huang and Shen proved a theorem of existence and uniqueness of solution for the equation u′′ f t, u t e t 0 14 under the weaker conditions than those in 13 . Stimulated by the works in 13, 14 , in the present paper, we investigate the solutions of the boundary value problems of Duffing equations with non-C2 perturbation functions at nonresonance using the minimax theorem proved by Huang in 15 .