µ pseudo rotating-periodic solutions for differential equations

Authors

  • Dandan Li Department of Mathematics Northeast Normal University
  • Jiayin Du Department of Mathematics Jilin University

DOI:

https://doi.org/10.58997/ejde.2020.43

Keywords:

Mu pseudo rotating periodic functions; exponential dichotomy.

Abstract

In this article, we combine rotating periodic functions with \(\mu\) ergodic functions to obtain a new class of functions called \(\mu\) pseudo rotating periodic functions. Then we study the existence and uniqueness of \(\mu\) pseudo rotating periodic solutions for linear systems, semi-linear systems, and non-linear systems by exponential dichotomy.

For more information see https://ejde.math.txstate.edu/Volumes/2020/43/abstr.html

References

E. Ait Dads, K. Ezzinbi, O. Arino; Pseudo almost periodic solutions for some differential equations in a Banach space, Nonlinear Anal., 28 (1997), 1141-1155. https://doi.org/10.1016/S0362-546X(97)82865-9

S. Bochner; Curvature and Betti numbers in real and complex vector bundles, Univ. e Politec. Torino. Rend. Sem. Mat., 15 (1955-56), 225-253.

S. Bochner; Uniform convergence of monotone sequences of functions, Proc. Nat. Acad. Sci. USA, 47 (1961), 582-585. https://doi.org/10.1073/pnas.47.4.582

J. Blot, P. Cieutat, K. Ezzinbi; New approach for weighted pseudo-almost periodic functions under the light of measure theory, basic results and applications, Appl. Anal. 92 (2013), 493-526. https://doi.org/10.1080/00036811.2011.628941

H. Bohr; Zur theorie der fast periodischen funktionen I, Acta Math., 45 (1925), 29-127. https://doi.org/10.1007/BF02395468

J. Campos, M. Tarallo; Almost automorphic linear dynamics by Favard theory, J. Differential Equations, 256 (2014), 1350-1367. https://doi.org/10.1016/j.jde.2013.10.018

C. Cheng, F. Huang, Y. Li; Affine-periodic solutions and pseudo affine-periodic solutions for differential equations with exponential dichotomy and exponential trichotomy, J. Appl. Anal. Comput. 6 (2016), 950-967. https://doi.org/10.11948/2016062

W. A. Coppel; Dichotomy and reducibility, J. Differential Equations, 3 (1967), 500-521. https://doi.org/10.1016/0022-0396(67)90014-9

T. Diagana; Weighted pseudo-almost periodic solutions to some differential equations, Nonlinear Anal. 68 (2008), 2250-2260. https://doi.org/10.1016/j.na.2007.01.054

H. Ding, T. Xiao, J. Liang; Asymptotically almost automorphic solutions for some integrodifferential equations with nonlocal initial conditions, J. Math. Anal. Appl., 338 (2008), 141-151 https://doi.org/10.1016/j.jmaa.2007.05.014

Z. Fan, J. Liang, T. Xiao; Composition of Stepanov-like pseudo almost automorphic functions and applications to nonautonomous evolution equations, Nonlinear Anal. Real World Appl., 13 (2012), 131-140. https://doi.org/10.1016/j.nonrwa.2011.07.019

J. K. Hale; Ordinary Differential Equations, Wiley-interscience New York, 1969.

J. Liang, J. Zhang, T. Xiao; Composition of pseudo almost automorphic and asymptotically almost automorphic functions, J. Math. Anal. Appl., 340 (2008) , 1493-1499. https://doi.org/10.1016/j.jmaa.2007.09.065

G. Liu, Y. Li, X. Yang; Existence and multiplicity of rotating periodic solutions for resonant Hamiltonian systems, J. Differential Equations, 265 (2018) , 1324-1352. https://doi.org/10.1016/j.jde.2018.04.001

G. Liu, Y. Li, X. Yang; Rotating periodic solutions for asymptotically linear second-order Hamiltonian systems with resonance at infinity, Math. Methods Appl. Sci., 40 (2017), 7139-7150. https://doi.org/10.1002/mma.4518

I. Newton; Philosophiae naturalis principia mathematica, Vol. I, Reprinting of the third edition with variant readings. Canbridge, Mass: Harvard University Press, 1972.

W. Shen, Y. Yi; Almost automorphic and almost periodic dynamics in skew-product semiflows, Mem. Amer. Math. Soc. 136 (1998) , x+93 pp. https://doi.org/10.1090/memo/0647

W. A. Veech; Almost automorphic functions on groups, Amer. J. Math., 87 (1965), 719-751. https://doi.org/10.2307/2373071

Y. Wang, Y. Li; Alternative theorems for pseudo almost automorphic problems, Taiwanese J. Math., 15 (2011) , 59-74. https://doi.org/10.11650/twjm/1500406161

H. Wang, X. Yang, Y. Li; Rotating-symmetric solutions for nonlinear systems with symmetry, Acta Math. Appl., 31 (2015), 307-312. https://doi.org/10.1007/s10255-015-0484-2

T. Xiao, J. Liang, J. Zhang; Pseudo almost automorphic solutions to semilinear differential equations in Banach spaces, Semigroup Forum. 76 (2008), 518-524. https://doi.org/10.1007/s00233-007-9011-y

J. Xing, X. Yang, Y. Li; Rotating periodic solutions for convex Hamiltonian systems, Appl. Math. Lett., 89 (2019), 91-96. https://doi.org/10.1016/j.aml.2018.10.002

H. J. Yang, X. L. Han; Existence and multiplicity of positive periodic solutions for fourth order nonlinear differential equations, Electron. J. Differential Equations, 2019 (2019) no. 119, 1-14.

X. Yang, Y. Zhang, Y. Li; Existence of rotating-periodic solutions for nonlinear systems via upper and lower solutions, Rocky Mountain J. Math., 47 (2017), 2423-2438. https://doi.org/10.1216/RMJ-2017-47-7-2423

Z. Yu, X.Yang, Y. Li; Affine-periodic solutions for dissipative systems, Abstr. Appl. Anal., (2013). https://doi.org/10.1155/2013/157140

C. Zhang; Pseudo-almost-periodic solutions of some differential equations, J. Math. Anal. Appl., 181 (1994), 62-76. https://doi.org/10.1006/jmaa.1994.1005

Downloads

Published

2020-05-16

Issue

Section

Articles

Categories

How to Cite

µ pseudo rotating-periodic solutions for differential equations. (2020). Electronic Journal of Differential Equations, 2020(01-132), No. 43, 1-11. https://doi.org/10.58997/ejde.2020.43