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Existence Theory for Integrodifferential Equations and Henstock-Kurzweil Integral in Banach Spaces

Aneta Sikorska-Nowak
2007 Journal of Applied Mathematics  
We prove existence theorems for the integrodifferential equationx'(t)=f(t,x(t),∫0tk(t,s,x(s))ds),x(0)=x0,t∈Ia=[0,a],a>0, wheref,k,xare functions with values in a Banach spaceEand the integral is taken  ...  in the sense of HL.  ...  This means that there exists a solution of the problem (1.1). Aneta Sikorska-Nowak 11  ... 
doi:10.1155/2007/31572 fatcat:7ysbc6q7ufezzi3vhgxhtruszi

Existence of Weak Solutions for Fractional Integrodifferential Equations with Multipoint Boundary Conditions

Haide Gou, Baolin Li
2018 International Journal of Differential Equations  
integrodifferential equations.  ...  By combining the techniques of fractional calculus with measure of weak noncompactness and fixed point theorem, we establish the existence of weak solutions of multipoint boundary value problem for fractional  ...  Introduction In recent years, fractional differential equations in Banach spaces have been studied and a few papers consider fractional differential equations in reflexive Banach spaces equipped with the  ... 
doi:10.1155/2018/1203031 fatcat:kauaoz3cp5awjgr76marvxbepy

Integrodifferential Equations on Time Scales with Henstock-Kurzweil-Pettis Delta Integrals

Aneta Sikorska-Nowak
2010 Abstract and Applied Analysis  
The functions are weakly-weakly sequentially continuous with values in a Banach space , and the integral is taken in the sense of Henstock-Kurzweil-Pettis delta integral.  ...  This integral generalizes the Henstock-Kurzweil delta integral and the Pettis integral.  ...  In 29 Cichoń introduce a definition of the Henstock-Kurzweil delta integral HK-Δintegral and HL delta integral HL-Δ-integral on Banach spaces for checking the existence of solutions of differential or  ... 
doi:10.1155/2010/836347 fatcat:votmfjwhgzayhg2hgfd3rx4mnu

Page 8973 of Mathematical Reviews Vol. , Issue 2002M [page]

2002 Mathematical Reviews  
McKibben (Baltimore, MD) 2002m:34111 34K30 26A39 34A60 Sikorska-Nowak, Aneta (PL-POZNM; Poznan) Retarded functional differential equations in Banach spaces and Henstock-Kurzweil integrals.  ...  She transcribes the equation into in- tegral form and introduces the HL integral, which is the Kurzweil- Henstock integral modified in such a way that the Saks-Henstock lemma is valid (which is not the  ... 

Page 291 of Mathematical Reviews Vol. , Issue 99a [page]

1991 Mathematical Reviews  
integral equation and the Henstock-Kurzweil integral.  ...  to quasilinear integrodifferential equations in Banach spaces.  ... 

Weak solutions nonlinear fractional integrodifferential equations in nonreflexive Banach spaces

Baolin Li, Haide Gou
2016 Boundary Value Problems  
The aim of this paper is to discuss the existence of weak solutions for a nonlinear two-point boundary value problem of integrodifferential equations of fractional order α ∈ (1, 2].  ...  MSC: 26A39; 35D30; 45B05; 35S15 Keywords: weak solutions; Henstock-Kurzweil-Pettis integral; Caputo fractional derivative; measure of weak noncompactness; boundary value problem c D α + x(t) = f (t, x  ...  Acknowledgements The authors wish to thank the referees for their endeavors and valuable comments. This work is supported by National Natural Science Foundation of China (11061031).  ... 
doi:10.1186/s13661-016-0716-2 fatcat:tfu24k3dhfellfgmjxppapddhi

Page 2484 of Mathematical Reviews Vol. , Issue 2003d [page]

2003 Mathematical Reviews  
The following modification of the definition of the Kurzweil-Henstock integral for functions f: R — X is considered: f is K*-integrable and J € X is its K*-integral if for every « > 0 there exist a gauge  ...  Let R be a compact interval in R” and X a Banach space.  ... 

Some Classes of Function Spaces, Their Properties, and Applications

Józef Banaś, Janusz Matkowski, Nelson Merentes, Manuel Pinto, Jose Luis Sanchez
2013 Journal of Function Spaces and Applications  
Méndez et al. contains a few results concerning the completion of the space of functions which are Henstock-Kurzweil integrable. The authors consider that space with the so-called Alexiewicz norm.  ...  equations, integral equations, functional differential, functional integral and functional equations, operator equations, and so forth.  ...  We hope that the results included in this issue will be an inspiration for researchers working in the theory of function spaces and nonlinear analysis.  ... 
doi:10.1155/2013/360980 fatcat:wbx74s7dpfhe3i2vfg7ndtwtje

Page 720 of Mathematical Reviews Vol. , Issue Subject Index [page]

Mathematical Reviews  
2002k:34158 Sikorska-Nowak, Aneta Retarded functional differential equations in Banach spaces and Henstock-Kurzweil integrals.  ...  Existence results on infinite intervals for neutral functional differential and integrodifferential inclusions in Banach spaces.  ... 

Page 737 of Mathematical Reviews Vol. , Issue Subject Index [page]

Mathematical Reviews  
Henstock-Kurzweil and Henstock- Kurzweil-Pettis integrals and some existence theorems. (see 2001d:00033) Domokos, A.  ...  .) *& Nonlinear differential equations in ordered spaces. 2001e:34112 Chai, Guo Qing (with Hu, Song Lin) Existence and uniqueness of solution of differential equations in Banach spaces. (Chinese.  ... 

Page 705 of Mathematical Reviews Vol. 32, Issue Index [page]

Mathematical Reviews  
equations with unbounded delay and Henstock-Kurzweil integrals.  ...  (English summary) 2000g:39007 Liu, Xinzhi (with Guo, Da Jun) Method of upper and lower solutions for second- order impulsive integro-differential equations in a Banach space.  ... 

Page 884 of Mathematical Reviews Vol. 31, Issue Index [page]

Mathematical Reviews  
Existence theorems for fractional set-valued integral equations in Banach spaces.  ...  (English summary) 994:45007 — Existence of solutions for Volterra integral equations in Banach spaces and monotone iterative techniques. (Chinese.  ... 

Page 584 of Mathematical Reviews Vol. , Issue Index [page]

Mathematical Reviews  
On retarded functional- differential equations and Henstock-Kurzweil integrals.  ...  (with Guo, Da Jun) Method of upper and lower solutions for nonlinear integrodifferential equations of mixed type in Banach spaces.  ...