Navier-Stokes equations: Some questions related to the direction of the vorticity
DCDS-S Home
Singular solutions of a nonlinear equation in a punctured domain of $\mathbb{R}^{2}$
April 2019, 12(2): 189-202. doi: 10.3934/dcdss.2019013
On solutions of semilinear upper diagonal infinite systems of differential equations
Józef Banaś 1,, and Monika Krajewska 2,
Department of Nonlinear Analysis, Rzeszów University of Technology, Al. Powstańców Warszawy 8, 35-959 Rzeszów, Poland
Institute of Economic and Management, State Higher School of Technology and Economics in Jarosław, ul. Czarnieckiego 16, 37-500 Jarosław, Poland
* Corresponding author: Józef Banaś
Dedicated to Professor Vicentiu Radulescu on the occasion of his 60th anniversary
Received August 2017 Revised December 2017 Published August 2018
The goal of the paper is to investigate the existence of solutions for semilinear upper diagonal infinite systems of differential equations. We will look for solutions of the mentioned infinite systems in a Banach tempered sequence space. In our considerations we utilize the technique associated with the Hausdorff measure of noncompactness and some existence results from the theory of ordinary differential equations in abstract Banach spaces.
Keywords: Infinite system of differential equation, Banach space, tempered sequence, semilinear upper diagonal infinite syatem of differential equations, measure of noncompactness.
Mathematics Subject Classification: Primary: 34G20; Secondary: 47H08.
Citation: Józef Banaś, Monika Krajewska. On solutions of semilinear upper diagonal infinite systems of differential equations. Discrete & Continuous Dynamical Systems - S, 2019, 12 (2) : 189-202. doi: 10.3934/dcdss.2019013
R. R. Akhmerov, M. I. Kamenskii, A. S. Potapov, A. E. Rodkina and B. N. Sadovskii, Measures of Noncompactness and Condensing Operators, Birkhäuser, Basel, 1992. doi: 10.1007/978-3-0348-5727-7. Google Scholar
J. M. Ayerbe Toledano, T. Dominguez Benavides and G. Lopez Acedo, Measures of Noncompactness in Metric Fixed Point Theory, Birkhäuser, Basel, 1997. doi: 10.1007/978-3-0348-8920-9. Google Scholar
J. Banaś and K. Goebel, Measures of Noncompactness in Banach Spaces, Marcel Dekker, New York, 1980. Google Scholar
J. Banaś and M. Krajewska, Existence of solutions for infinite systems of differential equations in spaces of tempered sequences, Electronic J. Differential Equations, 2017 (2017), 1-28. Google Scholar
J. Banaś and M. Mursaleen, Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations, Springer, New Delhi, 2014. doi: 10.1007/978-81-322-1886-9. Google Scholar
L. Cheng, Q. Cheng, Q. Shen, K. Tu and W. Zhang, A new approach to measures of noncompactness of Banach spaces, Studia Math., 240 (2018), 21-45. doi: 10.4064/sm8448-2-2017. Google Scholar
K. Deimling, Ordinary Differential Equations in Banach Spaces, Springer, Berlin, 1977. Google Scholar
K. Deimling, Nonlinear Functional Analysis, Springer, Berlin, 1985. doi: 10.1007/978-3-662-00547-7. Google Scholar
J. Mallet-Paret and R. D. Nussbaum, Inequivalent measures of noncompactness, Ann. Mat. Pura Appl., 190 (2011), 453-488. doi: 10.1007/s10231-010-0158-x. Google Scholar
H. Mönch and G. H. von Harten, On the Cauchy problem for ordinary differential equations in Banach spaces, Arch. Math., 39 (1982), 153-160. doi: 10.1007/BF01899196. Google Scholar
show all references
Hai Huang, Xianlong Fu. Optimal control problems for a neutral integro-differential system with infinite delay. Evolution Equations & Control Theory, 2020 doi: 10.3934/eect.2020107
Fabio Camilli, Giulia Cavagnari, Raul De Maio, Benedetto Piccoli. Superposition principle and schemes for measure differential equations. Kinetic & Related Models, 2021, 14 (1) : 89-113. doi: 10.3934/krm.2020050
Rim Bourguiba, Rosana Rodríguez-López. Existence results for fractional differential equations in presence of upper and lower solutions. Discrete & Continuous Dynamical Systems - B, 2021, 26 (3) : 1723-1747. doi: 10.3934/dcdsb.2020180
Youshan Tao, Michael Winkler. Critical mass for infinite-time blow-up in a haptotaxis system with nonlinear zero-order interaction. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 439-454. doi: 10.3934/dcds.2020216
Fathalla A. Rihan, Hebatallah J. Alsakaji. Stochastic delay differential equations of three-species prey-predator system with cooperation among prey species. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020468
Yukihiko Nakata. Existence of a period two solution of a delay differential equation. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 1103-1110. doi: 10.3934/dcdss.2020392
Lorenzo Zambotti. A brief and personal history of stochastic partial differential equations. Discrete & Continuous Dynamical Systems - A, 2021, 41 (1) : 471-487. doi: 10.3934/dcds.2020264
Siyang Cai, Yongmei Cai, Xuerong Mao. A stochastic differential equation SIS epidemic model with regime switching. Discrete & Continuous Dynamical Systems - B, 2020 doi: 10.3934/dcdsb.2020317
Ryuji Kajikiya. Existence of nodal solutions for the sublinear Moore-Nehari differential equation. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1483-1506. doi: 10.3934/dcds.2020326
Tetsuya Ishiwata, Young Chol Yang. Numerical and mathematical analysis of blow-up problems for a stochastic differential equation. Discrete & Continuous Dynamical Systems - S, 2021, 14 (3) : 909-918. doi: 10.3934/dcdss.2020391
Yueyang Zheng, Jingtao Shi. A stackelberg game of backward stochastic differential equations with partial information. Mathematical Control & Related Fields, 2020 doi: 10.3934/mcrf.2020047
Stefan Ruschel, Serhiy Yanchuk. The spectrum of delay differential equations with multiple hierarchical large delays. Discrete & Continuous Dynamical Systems - S, 2021, 14 (1) : 151-175. doi: 10.3934/dcdss.2020321
John Mallet-Paret, Roger D. Nussbaum. Asymptotic homogenization for delay-differential equations and a question of analyticity. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3789-3812. doi: 10.3934/dcds.2020044
Mugen Huang, Moxun Tang, Jianshe Yu, Bo Zheng. A stage structured model of delay differential equations for Aedes mosquito population suppression. Discrete & Continuous Dynamical Systems - A, 2020, 40 (6) : 3467-3484. doi: 10.3934/dcds.2020042
Bixiang Wang. Mean-square random invariant manifolds for stochastic differential equations. Discrete & Continuous Dynamical Systems - A, 2021, 41 (3) : 1449-1468. doi: 10.3934/dcds.2020324
Kerioui Nadjah, Abdelouahab Mohammed Salah. Stability and Hopf bifurcation of the coexistence equilibrium for a differential-algebraic biological economic system with predator harvesting. Electronic Research Archive, 2021, 29 (1) : 1641-1660. doi: 10.3934/era.2020084
Thabet Abdeljawad, Mohammad Esmael Samei. Applying quantum calculus for the existence of solution of $ q $-integro-differential equations with three criteria. Discrete & Continuous Dynamical Systems - S, 2020 doi: 10.3934/dcdss.2020440
Guangjun Shen, Xueying Wu, Xiuwei Yin. Stabilization of stochastic differential equations driven by G-Lévy process with discrete-time feedback control. Discrete & Continuous Dynamical Systems - B, 2021, 26 (2) : 755-774. doi: 10.3934/dcdsb.2020133
Editorial Office. Retraction: Xiao-Qian Jiang and Lun-Chuan Zhang, A pricing option approach based on backward stochastic differential equation theory. Discrete & Continuous Dynamical Systems - S, 2019, 12 (4&5) : 969-969. doi: 10.3934/dcdss.2019065
PDF downloads (107)
HTML views (102)
Józef Banaś Monika Krajewska
Article outline