S-ASYMPTOTICALLY BLOCH TYPE PERIODIC SOLUTIONS TO SOME SEMI-LINEAR EVOLUTION EQUATIONS IN BANACH SPACES

doi:10.1007/s10473-021-0206-1

Acta mathematica scientia,Series B ›› 2021, Vol. 41 ›› Issue (2): 413-425.doi: 10.1007/s10473-021-0206-1

• Articles • Previous Articles Next Articles

S-ASYMPTOTICALLY BLOCH TYPE PERIODIC SOLUTIONS TO SOME SEMI-LINEAR EVOLUTION EQUATIONS IN BANACH SPACES

Yong-Kui CHANG, Yanyan WEI

School of Mathematics and Statistics, Xidian University, Xi'an 710071, China

Received:2019-10-08 Revised:2020-10-26 Online:2021-04-25 Published:2021-04-29
About author:Yong-Kui CHANG,E-mail:ykchang@xidian.edu.cn,lzchangyk@163.com; Yanyan WEI,E-mail:yywei@stu.xidian.edu.cn
Supported by:
This work was partially supported by NSF of Shaanxi Province (2020JM-183).

Abstract

Abstract: This paper is mainly concerned with the $S$-asymptotically Bloch type periodicity. Firstly, we introduce a new notion of $S$-asymptotically Bloch type periodic functions, which can be seen as a generalization of concepts of $S$-asymptotically $\omega$-periodic functions and $S$-asymptotically $\omega$-anti-periodic functions. Secondly, we establish some fundamental properties on $S$-asymptotically Bloch type periodic functions. Finally, we apply the results obtained to investigate the existence and uniqueness of $S$-asymptotically Bloch type periodic mild solutions to some semi-linear differential equations in Banach spaces.

Key words: S-asymptotically Bloch type periodic functions, S-asymptotically ω antiperiodic functions, evolution equations

CLC Number:

34C25

Yong-Kui CHANG, Yanyan WEI. S-ASYMPTOTICALLY BLOCH TYPE PERIODIC SOLUTIONS TO SOME SEMI-LINEAR EVOLUTION EQUATIONS IN BANACH SPACES[J].Acta mathematica scientia,Series B, 2021, 41(2): 413-425.

Trendmd

References

[1] Hasler M F, N'Guérékata G M. Bloch-periodic functions and some applications. Nonlinear Stud, 2014, 21:21-30
[2] Oueama-Guengai E R, N'Guérékata G M. On S-asymptotically ω-periodic and Bloch periodic mild solutions to some fractional differential equations in abstract spaces. Math Meth Appl Sci, 2018, 41:9116-9122
[3] Li Q, Wang W, Teng K, et al. Ground states for fractional Schrödinger equations with electromagnetic fields and critical growth. Acta Mathematica Scientia, 2020, 40B(1):59-74
[4] Zheng X, Shang Y, Peng X. Orbital stability of periodic traveling wave solutions to the generalized Zakharov equations. Acta Mathematica Scientia, 2017, 37B(4):998-1018
[5] Gao H, Wang K, Wei F, et al. Massera-type theorem and asymptotically periodic logisitc equations. Nonlinear Anal RWA, 2006, 7:1268-1283
[6] Henríquez H R, Pierri M, Táboas P. On S-asymptotically ω-periodic functions on Banach spaces and applications. J Math Anal Appl, 2008, 343:1119-1130
[7] Pierri M. On S-asymptotically ω-periodic functions and applications. Nonliner Anal, 2012, 75:651-661
[8] Cuevas C, Souza de J. C. Existence of S-asymptotically ω-periodic solutions for fractional order functional integro-differential equations with infinite delay. Nonlinear Anal, 2010, 72:1683-1689
[9] Henríquez H R, Cuevas C, Caicedo A. Asymptotically periodic solutions of neutral partial differential equations with infinite delay. Comm Pure Appl Anal, 2013, 12:2031-2068
[10] Xia Z, Wang D, Wen C F, et al. Pseudo asymptotically periodic mild solutions of semilinear functional integro-differential equations in Banach spaces. Math Meth Appl Sci, 2017, 40:7333-7355
[11] Cao J, Yang Q, Huang Z. Existence of anti-periodic mild solutions for a class of semilinear fractional differential equations. Commun Nonlinear Sci Numer Simulat, 2012, 17:277-283
[12] Meyers M A, Chawla K K. Mechanical Behavior of Materials. Cambridge:Cambridge University Press, 2009
[13] Chang Y K, Ponce R. Uniform exponential stability and its applications to bounded solutions of integrodifferential equations in Banach spaces. J Integral Equations Appl, 2018, 30:347-369
[14] Cuevas C, Lizama C. Almost automorphic solutions to a class of semilinear fractional differential equations. Appl Math Lett, 2008, 21:1315-1319
[15] Lizama C, Poblete F. Regularity of mild solutions for a class of fractional order differential equations. Appl Math Comput, 2013, 224:803-816
[16] Cuesta E. Asymptotic behaviour of the solutions of fractional integro-differential equations and some time discretizations. Discrete Contin Dyn Syst, 2007, (Suppl):277-285
[17] Chang Y K, Ponce R, Rueda S. Fractional differential equations of Sobolev type with sectorial operators. Semigroup Forum, 2019, 99:591-606
[18] Arendt W, Batty C, Hieber M, et al. Vector-Valued Laplace Transforms and Cauchy Problems. Birkhäuser:Basel, 2001

S-ASYMPTOTICALLY BLOCH TYPE PERIODIC SOLUTIONS TO SOME SEMI-LINEAR EVOLUTION EQUATIONS IN BANACH SPACES

PDF (PC)

Abstract

Cite this article

share this article

References

Related Articles 5

Metrics

Comments

Recommended 0

[1]	Jing CUI, Litan YAN. CONTROLLABILITY OF NEUTRAL STOCHASTIC EVOLUTION EQUATIONS DRIVEN BY FRACTIONAL BROWNIAN MOTION [J]. Acta mathematica scientia,Series B, 2017, 37(1): 108-118.
[2]	Mina JIANG, Jianlin XIANG. ASYMPTOTIC STABILITY OF TRAVELING WAVES FOR A DISSIPATIVE NONLINEAR EVOLUTION SYSTEM [J]. Acta mathematica scientia,Series B, 2015, 35(6): 1325-1338.
[3]	PENG Yan. BOUNDARY LAYER AND VANISHING DIFFUSION LIMIT FOR NONLINEAR EVOLUTION EQUATIONS [J]. Acta mathematica scientia,Series B, 2014, 34(4): 1271-1286.
[4]	XIA Xue-Wen, LIU Kai. ON EXPONENTIAL STABILITY OF NON-AUTONOMOUS STOCHASTIC SEMILINEAR EVOLUTION EQUATIONS [J]. Acta mathematica scientia,Series B, 2002, 22(2): 178-188.
[5]	LIU Zhen-Hai, Ivan Szanto. MULTIVALUED DIFFERENTIAL EQUATIONS IN BANACH SPACES AND THEIR APPLICATIONS [J]. Acta mathematica scientia,Series B, 2002, 22(2): 213-221.