一类微分包含问题的伪概自守解

Abstract

Abstract:

This paper is dedicated to the study of the pseudo-almost automorphic $ C^0 $-solutions to a class of differential inclusion problems which have mixed nonlocal plus local initial conditions. Baseing on the fixed point theorem, theory of operator semigroups, and the properties of pseudo-almost automorphic functions, using $ \varepsilon $-discretisation techniques the existence of $ C^0 $-solutions for differential inclusion is discussed directly in the space which is composed by all pseudo-almost automorphic functions.

Key words: Pseudo almost automorphy $ C^0 $-solution, Differential inclusion, Mix initial conditions

CLC Number:

0175.1

Ye Li, Liu Yongjian, Liu Aimin. Pseudo-Almost Automorphic Solutions to A Class of Differential Inclusions[J].Acta mathematica scientia,Series A, 2024, 44(6): 1485-1498.

Trendmd

References 21

[1]	Aubin J P, Cellina A. Differential Inclusions. Berlin: Springer-Verlag, 1984
[2]	Tolstonogov A. Differential Inclusions in A Banach Space. Netherland: Kluwer Academic, 2000
[3]	Wang K, Michel A N. Stability analysis of differential inclusions in Banach space with applications to nonlinear systems with time delays. IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications, 1996, 43(8): 617-626
[4]	Aizicovici S, Papageorgiou N S, Staicu V. Periodic solutions of nonlinear evolution inclusions in Banach spaces. Journal of Nonlinear and Convex Analysis, 2006, 7(2): 1-19
[5]	Paicu A. Periodic solutions for a class of differential inclusions in general Banach spaces. Journal of Mathematical Analysis and Applications, 2008, 337(2): 1238-1248
[6]	Liu G F, Liu Y L. Anti-periodic solutions for differential inclusions in Banach spaces and their applications. Acta Math Sci, 2012, 32B(4): 1426-1434
[7]	邹瑶, 曾春娜, 胡进. 具有不连续激活函数的复数神经网络的全局指数周期性. 数学物理学报, 2019, 39A(5): 1192-1204
	Zou Y, Zeng C N, Hu J. Global exponential periodicity of complex-valued neural networks with discontinuous activation functions. Acta Math Sci, 2019, 39A(5): 1192-1204
[8]	Paicu A. Periodic solutions for a class of nonlinear evolution equations in Banach spaces. An Ştiint Univ Al I Cuza IaŞi Mat, 2009, 55(1): 107-118
[9]	Abbas S, Dhama S, Pinto M, Sepúlveda D. Pseudo compact almost automorphic solutions for a family of delayed population model of Nicholson type. Journal of Mathematical Analysis and Applications, 2021, 495(1): 124722
[10]	Wang C, Agarwal R P. Almost automorphic functions on semigroups induced by complete-closed time scales and application to dynamic equations. Discrete & Continuous Dynamical Systems-Series B, 2020, 25(2): 781-798
[11]	Vrabie I I. Almost periodic solutions for nonlinear delay evolutions with nonlocal initial conditions. Journal of Evolution Equations, 2013, 13: 693-714
[12]	Barbu V. Nonlinear Differential Equations of Monotone Types in Banach Spaces. Berlin: Springer Science & Business Media, 2010
[13]	Meknani B, Zhang J, Abdelhamid T. Pseudo-almost periodic $ C^0 $ solutions to the evolution equations with nonlocal initial conditions. Applicable Analysis, 2021, 102(3): 1-11
[14]	Burlicǎ M D, Roşu D. A class of nonlinear delay evolution equations with nonlocal initial conditions. Proceedings of the American Mathematical Society, 2014, 142(7): 2445-2458
[15]	Ye L, Liu Y J. Pseudo-almost periodic $C^{0} $-solution for evolution inclusion with mixed nonlocal plus local initial conditions. Hacettepe Journal of Mathematics and Statistics, 52(6): 1480-1491
[16]	N'Guérékata G M. Topics in Almost Automorphy. New York: Springer-Verlag, 2005
[17]	Amir B, Maniar L. Composition of pseudo almost periodic functions and Cauchy problems with operator of non dense domain. Annales Mathématiques Blaise Pascal. 1999, 6(1): 1-11
[18]	Liang J, N'Guérékata G M, Xiao T J, Zhang J. Some properties of pseudo-almost automorphic functions and applications to abstract differential equations. Nonlinear Analysis: Theory, Methods & Applications, 2009, 70(7): 2731-2735
[19]	Liang J, Zhang J, Xiao T J. Composition of pseudo almost automorphic and asymptotically almost automorphic functions. Journal of Mathematical Analysis and Applications, 2008, 340(2): 1493-1499
[20]	Kobayashi Y. Difference approximation of Cauchy problems for quasi-dissipative operators and generation of nonlinear semigroups. Journal of the Mathematical Society of Japan, 1975, 27(4): 640-665
[21]	Vrabie I I. Compactness Methods for Nonlinear Evolutions. London: Longman Scientific & Technical, 1995

Pseudo-Almost Automorphic Solutions to A Class of Differential Inclusions

RichHTML

PDF (PC)

Abstract

Cite this article

share this article

References 21

Related Articles 6

Metrics

Comments

Recommended 10

[1]	Yan Luo,Wenzhe Xie. Existence of Solutions for Impulsive Differential Inclusions with Upper and Lower Solutions in the Reverse Order [J]. Acta mathematica scientia,Series A, 2019, 39(5): 1055-1063.
[2]	Jum-Ran KANG. GENERAL DECAY FOR A DIFFERENTIAL INCLUSION OF KIRCHHOFF TYPE WITH A MEMORY CONDITION AT THE BOUNDARY [J]. Acta mathematica scientia,Series A, 2014, 34(3): 729-738.
[3]	DAI Guo-Wei, WANG Wen-Ting, FENG Li-Li. Nonsmooth Version of Dual Fountain Theorem and Its Application to a Differential Inclusion Problem [J]. Acta mathematica scientia,Series A, 2012, 32(3): 530-539.
[4]	GE Bin, XUE Xiao-Ping, ZHOU Qing-Mei. Multiple Solutions for a p(x)}-Kirchhoff-type Equation with Nonsmooth Potential [J]. Acta mathematica scientia,Series A, 2011, 31(5): 1431-1438.
[5]	Hong Shihuang. Nonlinear Boundary Value Problems for Differential Inclusions [J]. Acta mathematica scientia,Series A, 2007, 27(4): 711-719.
[6]	Qin Songxi, Wang Zhihua. Monotonic Trajectory of Differential Inclusions [J]. Acta mathematica scientia,Series A, 1998, 18(S1): 44-50.