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On the boundedness of solutions of the equation $u''+(1+f(t))u=0$
Centerstable manifolds for differential equations with statedependent delays
1.  Department of Mathematics and Statistics, York University, Toronto, Ontario, Canada M3J 1P3, Canada 
2.  Mathematisches Institut, Universität Gieβen, Arndtstr. 2, 35392 Gieβen 
[1] 
Tibor Krisztin. A local unstable manifold for differential equations with statedependent delay. Discrete and Continuous Dynamical Systems, 2003, 9 (4) : 9931028. doi: 10.3934/dcds.2003.9.993 
[2] 
Ovide Arino, Eva Sánchez. A saddle point theorem for functional statedependent delay differential equations. Discrete and Continuous Dynamical Systems, 2005, 12 (4) : 687722. doi: 10.3934/dcds.2005.12.687 
[3] 
Ismael Maroto, Carmen NÚÑez, Rafael Obaya. Dynamical properties of nonautonomous functional differential equations with statedependent delay. Discrete and Continuous Dynamical Systems, 2017, 37 (7) : 39393961. doi: 10.3934/dcds.2017167 
[4] 
Ismael Maroto, Carmen Núñez, Rafael Obaya. Exponential stability for nonautonomous functional differential equations with statedependent delay. Discrete and Continuous Dynamical Systems  B, 2017, 22 (8) : 31673197. doi: 10.3934/dcdsb.2017169 
[5] 
A. R. Humphries, O. A. DeMasi, F. M. G. Magpantay, F. Upham. Dynamics of a delay differential equation with multiple statedependent delays. Discrete and Continuous Dynamical Systems, 2012, 32 (8) : 27012727. doi: 10.3934/dcds.2012.32.2701 
[6] 
Xiuli Sun, Rong Yuan, Yunfei Lv. Global Hopf bifurcations of neutral functional differential equations with statedependent delay. Discrete and Continuous Dynamical Systems  B, 2018, 23 (2) : 667700. doi: 10.3934/dcdsb.2018038 
[7] 
Ferenc Hartung, Janos Turi. Linearized stability in functional differential equations with statedependent delays. Conference Publications, 2001, 2001 (Special) : 416425. doi: 10.3934/proc.2001.2001.416 
[8] 
Josef Diblík. Longtime behavior of positive solutions of a differential equation with statedependent delay. Discrete and Continuous Dynamical Systems  S, 2020, 13 (1) : 3146. doi: 10.3934/dcdss.2020002 
[9] 
Qingwen Hu, Bernhard LaniWayda, Eugen Stumpf. Preface: Delay differential equations with statedependent delays and their applications. Discrete and Continuous Dynamical Systems  S, 2020, 13 (1) : ii. doi: 10.3934/dcdss.20201i 
[10] 
Eugen Stumpf. Local stability analysis of differential equations with statedependent delay. Discrete and Continuous Dynamical Systems, 2016, 36 (6) : 34453461. doi: 10.3934/dcds.2016.36.3445 
[11] 
Hermann Brunner, Stefano Maset. Time transformations for statedependent delay differential equations. Communications on Pure and Applied Analysis, 2010, 9 (1) : 2345. doi: 10.3934/cpaa.2010.9.23 
[12] 
Matthias Büger, Marcus R.W. Martin. Stabilizing control for an unbounded statedependent delay equation. Conference Publications, 2001, 2001 (Special) : 5665. doi: 10.3934/proc.2001.2001.56 
[13] 
Jitai Liang, Ben Niu, Junjie Wei. Linearized stability for abstract functional differential equations subject to statedependent delays with applications. Discrete and Continuous Dynamical Systems  B, 2019, 24 (11) : 61676188. doi: 10.3934/dcdsb.2019134 
[14] 
HansOtto Walther. On Poisson's statedependent delay. Discrete and Continuous Dynamical Systems, 2013, 33 (1) : 365379. doi: 10.3934/dcds.2013.33.365 
[15] 
István Györi, Ferenc Hartung. Exponential stability of a statedependent delay system. Discrete and Continuous Dynamical Systems, 2007, 18 (4) : 773791. doi: 10.3934/dcds.2007.18.773 
[16] 
Jan Sieber. Finding periodic orbits in statedependent delay differential equations as roots of algebraic equations. Discrete and Continuous Dynamical Systems, 2012, 32 (8) : 26072651. doi: 10.3934/dcds.2012.32.2607 
[17] 
F. M. G. Magpantay, A. R. Humphries. Generalised LyapunovRazumikhin techniques for scalar statedependent delay differential equations. Discrete and Continuous Dynamical Systems  S, 2020, 13 (1) : 85104. doi: 10.3934/dcdss.2020005 
[18] 
Benjamin B. Kennedy. A statedependent delay equation with negative feedback and "mildly unstable" rapidly oscillating periodic solutions. Discrete and Continuous Dynamical Systems  B, 2013, 18 (6) : 16331650. doi: 10.3934/dcdsb.2013.18.1633 
[19] 
Guo Lin, Haiyan Wang. Traveling wave solutions of a reactiondiffusion equation with statedependent delay. Communications on Pure and Applied Analysis, 2016, 15 (2) : 319334. doi: 10.3934/cpaa.2016.15.319 
[20] 
Benjamin B. Kennedy. A periodic solution with nonsimple oscillation for an equation with statedependent delay and strictly monotonic negative feedback. Discrete and Continuous Dynamical Systems  S, 2020, 13 (1) : 4766. doi: 10.3934/dcdss.2020003 
2020 Impact Factor: 1.392
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