2003, 2003(Special): 672-677. doi: 10.3934/proc.2003.2003.672

On weak-almost periodic mild solutions of some linear abstract differential equations

1. 

Department of Mathematics, Morgan State University, Baltimore, Maryland 21251, United States

Received  July 2002 Revised  April 2003 Published  April 2003

We are concerned with the differential equation $x'(t) = Ax(t) + f(t)$ with a linear operator $A$ acting in a Banach space $X$ and $f : \mathbb(R) \to X$ a almost periodic function (in Bochner’s sense). We give necessary conditions to ensure that the so-called optimal mild solutions are also weakly almost periodic.
Citation: Gaston N'Guerekata. On weak-almost periodic mild solutions of some linear abstract differential equations. Conference Publications, 2003, 2003 (Special) : 672-677. doi: 10.3934/proc.2003.2003.672
[1]

Sonja Cox, Arnulf Jentzen, Ryan Kurniawan, Primož Pušnik. On the mild Itô formula in Banach spaces. Discrete and Continuous Dynamical Systems - B, 2018, 23 (6) : 2217-2243. doi: 10.3934/dcdsb.2018232

[2]

Yuri Latushkin, Valerian Yurov. Stability estimates for semigroups on Banach spaces. Discrete and Continuous Dynamical Systems, 2013, 33 (11&12) : 5203-5216. doi: 10.3934/dcds.2013.33.5203

[3]

Noriaki Yamazaki. Almost periodicity of solutions to free boundary problems. Conference Publications, 2001, 2001 (Special) : 386-397. doi: 10.3934/proc.2001.2001.386

[4]

Filippo Gazzola, Mirko Sardella. Attractors for families of processes in weak topologies of Banach spaces. Discrete and Continuous Dynamical Systems, 1998, 4 (3) : 455-466. doi: 10.3934/dcds.1998.4.455

[5]

Fatihcan M. Atay, Lavinia Roncoroni. Lumpability of linear evolution Equations in Banach spaces. Evolution Equations and Control Theory, 2017, 6 (1) : 15-34. doi: 10.3934/eect.2017002

[6]

Rui Zhang, Yong-Kui Chang, G. M. N'Guérékata. Weighted pseudo almost automorphic mild solutions to semilinear integral equations with $S^{p}$-weighted pseudo almost automorphic coefficients. Discrete and Continuous Dynamical Systems, 2013, 33 (11&12) : 5525-5537. doi: 10.3934/dcds.2013.33.5525

[7]

Jesus Idelfonso Díaz, Jean Michel Rakotoson. On very weak solutions of semi-linear elliptic equations in the framework of weighted spaces with respect to the distance to the boundary. Discrete and Continuous Dynamical Systems, 2010, 27 (3) : 1037-1058. doi: 10.3934/dcds.2010.27.1037

[8]

Sebti Kerbal, Yang Jiang. General integro-differential equations and optimal controls on Banach spaces. Journal of Industrial and Management Optimization, 2007, 3 (1) : 119-128. doi: 10.3934/jimo.2007.3.119

[9]

Wolfgang Arendt, Patrick J. Rabier. Linear evolution operators on spaces of periodic functions. Communications on Pure and Applied Analysis, 2009, 8 (1) : 5-36. doi: 10.3934/cpaa.2009.8.5

[10]

Tomás Caraballo, David Cheban. Almost periodic and almost automorphic solutions of linear differential equations. Discrete and Continuous Dynamical Systems, 2013, 33 (5) : 1857-1882. doi: 10.3934/dcds.2013.33.1857

[11]

Felipe Alvarez, Juan Peypouquet. Asymptotic equivalence and Kobayashi-type estimates for nonautonomous monotone operators in Banach spaces. Discrete and Continuous Dynamical Systems, 2009, 25 (4) : 1109-1128. doi: 10.3934/dcds.2009.25.1109

[12]

Priscila Santos Ramos, J. Vanterler da C. Sousa, E. Capelas de Oliveira. Existence and uniqueness of mild solutions for quasi-linear fractional integro-differential equations. Evolution Equations and Control Theory, 2022, 11 (1) : 1-24. doi: 10.3934/eect.2020100

[13]

Armin Lechleiter, Marcel Rennoch. Non-linear Tikhonov regularization in Banach spaces for inverse scattering from anisotropic penetrable media. Inverse Problems and Imaging, 2017, 11 (1) : 151-176. doi: 10.3934/ipi.2017008

[14]

Mustapha Mokhtar-Kharroubi. On permanent regimes for non-autonomous linear evolution equations in Banach spaces with applications to transport theory. Kinetic and Related Models, 2010, 3 (3) : 473-499. doi: 10.3934/krm.2010.3.473

[15]

X. Xiang, Y. Peng, W. Wei. A general class of nonlinear impulsive integral differential equations and optimal controls on Banach spaces. Conference Publications, 2005, 2005 (Special) : 911-919. doi: 10.3934/proc.2005.2005.911

[16]

Arunima Bhattacharya, Micah Warren. $ C^{2, \alpha} $ estimates for solutions to almost Linear elliptic equations. Communications on Pure and Applied Analysis, 2021, 20 (4) : 1363-1383. doi: 10.3934/cpaa.2021024

[17]

Kapil Kumar Choudhary, Rajiv Kumar, Rajesh Kumar. Global classical and weak solutions of the prion proliferation model in the presence of chaperone in a banach space. Evolution Equations and Control Theory, 2021  doi: 10.3934/eect.2021039

[18]

Goro Akagi, Mitsuharu Ôtani. Evolution equations and subdifferentials in Banach spaces. Conference Publications, 2003, 2003 (Special) : 11-20. doi: 10.3934/proc.2003.2003.11

[19]

Marina V. Plekhanova. Strong solutions of quasilinear equations in Banach spaces not solvable with respect to the highest-order derivative. Discrete and Continuous Dynamical Systems - S, 2016, 9 (3) : 833-846. doi: 10.3934/dcdss.2016031

[20]

Tôn Việt Tạ. Non-autonomous stochastic evolution equations in Banach spaces of martingale type 2: Strict solutions and maximal regularity. Discrete and Continuous Dynamical Systems, 2017, 37 (8) : 4507-4542. doi: 10.3934/dcds.2017193

 Impact Factor: 

Metrics

  • PDF downloads (51)
  • HTML views (0)
  • Cited by (0)

Other articles
by authors

[Back to Top]