Existence and multiplicity of positive periodic solutions for fourth-order nonlinear differential equations

Date

2019-11-14

Authors

Yang, Hujun
Han, Xiaoling

Journal Title

Journal ISSN

Volume Title

Publisher

Texas State University, Department of Mathematics

Abstract

In this article we study the existence and multiplicity of positive periodic solutions for two classes of non-autonomous fourth-order nonlinear ordinary differential equations uiv - pu″ - α(x)un + b(x)un+2 = 0, uiv - pu″ + α(x)un - b(x)un+2 = 0 where n is a positive integer, p ≤ 1, and α(x), b(x) are continuous positive T-periodic functions. These equations include particular cases of the extended Fisher-Kolmogorov equations and the Swift-Hohenberg equations. By using Mawhin's continuation theorem, we obtain two multiplicity results these equations.

Description

Keywords

Fourth-order nonlinear differential equations, Multiplicity, Positive periodic solutions, Mawhin's continuation theorem

Citation

Yang, H., & Han, X. (2019). Existence and multiplicity of positive periodic solutions for fourth-order nonlinear differential equations. <i>Electronic Journal of Differential Equations, 2019</i>(119), pp. 1-14.

Rights

Attribution 4.0 International

Rights Holder

Rights License