References
- Aiello WG , Freedman HI , Wu J . Analysis of a model representing stage-structured population growth with state-dependent time delay. SIAM J Appl Math. 1992;52(3):855–869.
- Hartung F , Krisztin T , Walther H-O , et al. Functional differential equations with state-dependent delays: theory and applications. In: Handbook of differential equations: ordinary differential equations. Vol. III, Handbook of differential equations. Amsterdam: Elsevier/North-Holland; 2006. p. 435–545.
- Driver RD . A functional-differential system of neutral type arising in a two-body problem of classical electrodynamics. In: LaSalle J , Lefschtz S , editors. International symposium on nonlinear differential equations and nonlinear mechanics. New York (NY): Academic Press; 1963. p. 474–484.
- Driver RD . A neutral system with state-dependent delay. J Differ Equ. 1984;54:73–86.
- Hartung F . On differentiability of solutions with respect to parameters in neutral differential equations with state-dependent delays. Ann Mat Pura Appl (4). 2013;192(1):17–47.
- Hartung F , Turi J . On differentiability of solutions with respect to parameters in state-dependent delay equations. J Differ Equ. 1997;135(2):192–237.
- Hartung F . Differentiability of solutions with respect to parameters in neutral differential equations with state-dependent delays. J Math Anal Appl. 2006;324(1):504–524.
- Walther H-O . The solution manifold and C 1-smoothness for differential equations with state-dependent delay. J Differ Equ. 2003;195(1):46–65.
- Henríquez E , Prokopczyk A , Ladeira L . A note on partial functional differential equations with state-dependent delay. Nonlinear Anal Real World Appl. 2006;7(4):510–519.
- Rezounenko AV . A condition on delay for differential equations with discrete state-dependent delay. J Math Anal Appl. 2012;385(1):506–516.
- Rezounenko AV . Partial differential equations with discrete and distributed state-dependent delays. J Math Anal Appl. 2007;326(2):1031–1045.
- Rezounenko AV , Wu J . A non-local PDE model for population dynamics with state-selective delay: local theory and global attractors. J Comput Appl Math. 2006;190(1–2):99–113.
- Kosovalic N , Magpantay FMG , Chen Y , et al . Abstract algebraic-delay differential systems and age structured population dynamics. J Differ Equ. 2013;255(3):593–609.
- Krisztin T , Rezounenko A . Parabolic partial differential equations with discrete state-dependent delay: classical solutions and solution manifold. J Differ Equ. 2016;260(5):4454–4472.
- Lv Y , Rong Y , Yongzhen P . Smoothness of semiflows for parabolic partial differential equations with state-dependent delay. J Differ Equ. 2016;260:6201–6231.
- Kosovalic N , Chen Y , Wu J . Algebraic-delay differential systems: C 0-extendable submanifolds and linearization. Trans Amer Math Soc. 2017;369(5):3387–3419.
- Hernández E , Pierri M , Wu J . C 1+α -strict solutions and wellposedness of abstract differential equations with state dependent delay. J Differ Equ. 2016;261(12):6856–6882.
- Arthi G , Park JH , Jung HY . Existence and controllability results for second-order impulsive stochastic evolution systems with state-dependent delay. Appl Math Comput. 2014;248:328–341.
- Chueshov I , Rezounenko A . Dynamics of second order in time evolution equations with state-dependent delay. Nonlinear Anal Theory Methods Appl. 2015;123:126–149.
- Das S , Pandey DN , Sukavanam N . Approximate controllability of a second-order neutral stochastic differential equation with state-dependent delay. Nonlinear Anal Model Control. 2016;21(6):751–769.
- Das S , Pandey D , Sukavanam N . Existence of solution and approximate controllability of a second-order neutral stochastic differential equation with state dependent delay. Acta Math Sci Ser B Engl Ed. 2016;36(5):1509–1523.
- Das S , Pandey DN , Sukavanam N . Approximate controllability of a second order neutral differential equation with state dependent delay. Differ Equ Dyn Syst. 2016;24(2):201–214.
- Hernández E . Existence of solutions for a second order abstract functional differential equation with state-dependent delay. Electron J Differ Equ. 2007;21. 10 p.
- Radhakrishnan B , Balachandran K . Controllability of neutral evolution integrodifferential systems with state dependent delay. J Optim Theory Appl. 2012;153(1):85–97.
- Sakthivel R , Anandhi ER , Mahmudov NI . Approximate controllability of second-order systems with state-dependent delay. Numer Funct Anal Optim. 2008;29(11–12):1347–1362.
- Kisyński J . On cosine operator functions and one parameter group of operators. Studia Math. 1972;49.
- Fattorini HO . Second order linear differential equations in Banach spaces. Vol. 108, North-Holland mathematics studies. Amsterdam: North-Holland; 1985.
- Vasil’ev VV , Piskarev SI . Differential equations in Banach spaces. II. Theory of cosine operator functions. Functional analysis. J Math Sci (N Y). 2004;122(2):3055–3174.
- Travis CC , Webb GF . Compactness, regularity, and uniform continuity properties of strongly continuous cosine families. Houston J Math. 1977;3(4):555–567.
- Travis CC , Webb GF . Cosine families and abstract nonlinear second order differential equations. Acta Math Acad Sci Hungaricae. 1978;32:76–96.
- Diestel J , Uhl JJ . Vector measures. Providence (RI): American Mathematical Society; 1972.
- Henríquez H , Vásquez CH . Differentiabilty of solutions of the second order abstract Cauchy problem. Semigroup Forum. 2002;64(3):472–488.