Infinity of subharmonics for Duffing equations with convex and oscillatory nonlinearities
نویسندگان
چکیده
منابع مشابه
Infinity of subharmonics for Duffing equations with convex and oscillatory nonlinearities
*Correspondence: [email protected] 2School of Mathematical Sciences, Soochow University, Suzhou, 215006, China Full list of author information is available at the end of the article Abstract The existence of infinity of subharmonics for Duffing equations with convex and oscillatory nonlinearities is shown. This result is a corollary of two theorems. These theorems, one for a weak sub-quadratic...
متن کاملDuffing equations with cubic and quintic nonlinearities
In this study, an accurate analytical solution for Duffing equations with cubic and quintic nonlinearities is obtainedusing theHomotopyAnalysisMethod (HAM) andHomotopy Pade technique. Novel and accurate analytical solutions for the frequency and displacement are derived. Comparison between the obtained results andnumerical solutions shows that only the first order approximation of the Homotopy ...
متن کاملOscillatory Solutions of Neutral Equations with Polynomial Nonlinearities
In 1, 2 , we have considered a lossless transmission line terminated by a nonlinear resistive load and parallel connected capacitance cf. Figure 1 . The nonlinear boundary condition is caused by the polynomial type V-I characteristics of the nonlinear load at the second end of the transmission line cf. Figure 1 . The voltage and current u x, t , i x, t of the lossless transmission line can be f...
متن کاملStability and Exact Multiplicity of Periodic Solutions of Duffing Equations with Cubic Nonlinearities
We study the stability and exact multiplicity of periodic solutions of the Duffing equation with cubic nonlinearities, x + cx + ax − x = h(t), (∗) where a and c > 0 are positive constants and h(t) is a positive T -periodic function. We obtain sharp bounds for h such that (∗) has exactly three ordered T -periodic solutions. Moreover, when h is within these bounds, one of the three solutions is n...
متن کاملSubharmonics with Minimal Periods for Convex Discrete Hamiltonian Systems
and Applied Analysis 3 Lemma 6 (see [12, proposition 2.2]). LetH : R → R be of C 1 and convex functional, −β ≤ H(u) ≤ αq|u| + γ, where u ∈ R, α > 0, q > 1, β ≥ 0, γ ≥ 0. Then αp|∇H(u)| ≤ (∇H(u), u) + β + γ, where 1/p + 1/q = 1. In order to know the form of u ∈ E pT , we consider eigenvalue problem LJΔu (n − 1) = λu (n) , u (n + pT) = u (n) , (12) where u(n) = ( u1(n) u2(n) ), Lu(n − 1) = ( u1(n...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Boundary Value Problems
سال: 2016
ISSN: 1687-2770
DOI: 10.1186/s13661-016-0729-x