Abstract
This paper deals with a boundary value problem for Duffing equation. The existence of unique solution for the problem is studied by using the minimax theorem due to Huang Wenhua. The existence and uniqueness result was presented under a generalized nonresonance condition.
Highlights
Many authors are greatly attached to investigation for the existence and uniqueness of solution of Duffing equations, for example, 1–11, and so forth
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, 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
Summary
Many authors are greatly attached to investigation for the existence and uniqueness of solution of Duffing equations, for example, 1–11 , and so forth. Proved the existence and uniqueness of solution of Duffing equations under C2 perturbation functions and other conditions at nonresonance by employing minimax 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. 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 under the weaker conditions than those in 13. Stimulated by the works in 13, , 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
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