Access the full text.
Sign up today, get DeepDyve free for 14 days.
Loading next page...
/lp/springer-journals/nonlocal-integrated-solutions-for-a-class-of-abstract-evolution-6IkVW8ZTaT
References (39)
-
C. Lizama (1998)
A characterization of uniform continuity for Volterra equations in Hilbert spaces, 126
-
A. Pazy (1983)
Semigroups of Linear Operators and Applications to Partial Differential Equations -
J. Banaś, M. Mursaleen (2014)
Sequence Spaces and Measures of Noncompactness with Applications to Differential and Integral Equations -
R. Miller (1978)
An integrodifferential equation for rigid heat conductors with memoryJournal of Mathematical Analysis and Applications, 66
-
Yong Zhou, Rongnian Wang, Li Peng (2017)
Topological Structure of the Solution Set for Evolution Inclusions -
K. Deng (1993)
Exponential Decay of Solutions of Semilinear Parabolic Equations with Nonlocal Initial ConditionsJournal of Mathematical Analysis and Applications, 179
-
J. Banaś, Agnieszka Chlebowicz (2009)
On integrable solutions of a nonlinear Volterra integral equation under Carathéodory conditionsBulletin of the London Mathematical Society, 41
-
J. Banaś, M. Jleli, M. Mursaleen, B. Samet, C. Vetro (2017)
Advances in Nonlinear Analysis via the Concept of Measure of Noncompactness -
F. Bureau (1962)
The Cauchy problem for partial differential equations of the second order and the method of ascentJournal of Mathematical Analysis and Applications, 4
-
F.J. Bureau (1962)
The Cauchy problem for partial differential equations of the second order and the method of ascentJ. Comput. Appl. Math., 4
-
L. Byszewski (1990)
Existence and uniqueness of solutions of nonlocal problems for hyperbolic equation uxt=F(x,t,u,ux)Journal of Applied Mathematics and Stochastic Analysis, 3
-
K. Engel, R. Nagel (1999)
One-parameter semigroups for linear evolution equationsSemigroup Forum, 63
-
J. Prüss (1993)
Evolutionary Integral Equations And Applications -
J. Banaś, R. Nalepa (2016)
On a measure of noncompactness in the space of functions with tempered incrementsJournal of Mathematical Analysis and Applications, 435
-
A. Karczewska, C. Lizama (2014)
Stochastic Volterra equations under perturbationsElectronic Communications in Probability, 19
-
Aldo Pereira, Rodrigo Ponce (2015)
NORM CONTINUITY FOR STRONGLY CONTINUOUS FAMILIES OF OPERATORS -
J. Banaś (1980)
Measures of Noncompactness in Banach Spaces -
J. Prüss (2009)
Decay properties for the solutions of a partial differential equation with memoryArchiv der Mathematik, 92
-
R. Akhmerov, M. Kamenskiĭ, A. Potapov, A. Rodkina, B. Sadovskii (1992)
Measures of noncompactness and condensing operatorsOperator theory, 55
-
Lishan Liu, F. Guo, Congxin Wu, Yonghong Wu (2005)
Existence theorems of global solutions for nonlinear Volterra type integral equations in Banach spacesJournal of Mathematical Analysis and Applications, 309
-
Xiaosen Han, Mingxin Wang (2010)
General Decay Estimate of Energy for the Second Order Evolution Equations with MemoryActa Applicandae Mathematicae, 110
-
L. Byszewskik (1990)
Existence and uniqueness of solutions of nonlocal problems for hyperbolic equation u x t = F ( x , t , u , u x ) $u_{xt} = F(x, t, u, u_{x})$J. Appl. Math. Stoch. Anal., 3
-
Jung‐Chan Chang (2017)
Asymptotically periodic solutions of a partial differential equation with memoryJournal of Fixed Point Theory and Applications, 19
-
P. Olver (2007)
Introduction to Partial Differential Equations -
H. Henríquez, Verónica Poblete, Juan Pozo (2014)
Mild solutions of non-autonomous second order problems with nonlocal initial conditionsJournal of Mathematical Analysis and Applications, 412
-
Z. Fan (2014)
Characterization of compactness for resolvents and its applicationsAppl. Math. Comput., 232
-
J. Prüss (1987)
Positivity and regularity of hyperbolic Volterra equations in Banach spacesMathematische Annalen, 279
-
J. Banaś (2012)
Measures of noncompactness in the study of solutions of nonlinear differential and integral equationsCentral European Journal of Mathematics, 10
-
D. Bothe (1998)
Multivalued perturbations ofm-accretive differential inclusionsIsrael Journal of Mathematics, 108
-
W. Arendt, H. Kellermann (1987)
Integrated solutions of Volterra integrodifferential equations and applicationsPitman Res. Notes Math. Ser., 190
-
C. Lizama, Juan Pozo (2012)
Existence of Mild Solutions for a Semilinear Integrodifferential Equation with Nonlocal Initial ConditionsAbstract and Applied Analysis, 2012
-
W. Arendt, C. Batty (1996)
Almost Periodic Solutions of First- and Second-Order Cauchy ProblemsJournal of Differential Equations, 137
-
S. Aizicovici, V. Staicu (2007)
Multivalued evolution equations with nonlocal initial conditions in Banach spacesNonlinear Differential Equations and Applications NoDEA, 14
-
I. Vrabie (2012)
Existence in the large for nonlinear delay evolution inclusions with nonlocal initial conditionsJournal of Functional Analysis, 262
-
V. Luong (2016)
Decay mild solutions of the nonlocal Cauchy problem for second order evolution equations with memoryElectronic Journal of Qualitative Theory of Differential Equations
-
R. Wang, P. Zhu (2013)
Non-autonomous evolution inclusions with nonlocal history conditions: Global integral solutionsNonlinear Analysis-theory Methods & Applications, 85
-
P. Cannarsa, D. Sforza (2011)
Integro-differential equations of hyperbolic type with positive definite kernelsJournal of Differential Equations, 250
-
Fatiha Alabau-Boussouira, P. Cannarsa, D. Sforza (2008)
Decay estimates for second order evolution equations with memoryJournal of Functional Analysis, 254
-
S. Ana, P.Elav arasi (2018)
TopologyInternational Journal of Mathematics Trends and Technology
- Publisher
- Springer Journals
- Copyright
- Copyright © 2018 by Springer Nature B.V.
- Subject
- Mathematics; Computational Mathematics and Numerical Analysis; Applications of Mathematics; Partial Differential Equations; Probability Theory and Stochastic Processes; Calculus of Variations and Optimal Control; Optimization
- ISSN
- 0167-8019
- eISSN
- 1572-9036
- DOI
- 10.1007/s10440-018-00231-3
- Publisher site
- See Article on Publisher Site
Abstract
In this article we show the existence of at least one integrated solution of a semilinear second order differential equation with an extra convolution term and nonlocal initial conditions. As main tool we use properties of the Hausdorff measure of noncompactness and fixed point theorems.
Journal
Acta Applicandae Mathematicae – Springer Journals
Published: Dec 17, 2018