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