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Existence of unbounded solutions of a linear homogenous system of differential equations with two delays
An explicit coefficient criterion for the existence of positive solutions to the linear advanced equation
1. | Department of Mathematics and Descriptive Geometry, Faculty of Civil Engineering and Department of Mathematics, Faculty of Electrical Engineering and Communication, Brno University of Technology, Brno |
2. | Department of Difference Equations and Discrete Systems, Institute of Mathematics, University of Białystok, Białystok, Poland |
3. | Department of Mathematics, University of Žilina, Žilina, Slovak Republic |
References:
[1] |
R. P. Agarwal, L. Berezansky, E. Braverman and A. Domoshnitsky, Nonoscillation Theory of Functional Differential Equations with Applications, Springer, 2012.
doi: 10.1007/978-1-4614-3455-9. |
[2] |
R. P. Agarwal, M. Bohner and W.-T. Li, Nonoscillation and Oscillation: Theory for Functional Differential Equations, Marcel Dekker, Inc., 2004.
doi: 10.1201/9780203025741. |
[3] |
H. Bereketoǧlu, F. Karakoç and G. Seyhan, Oscillatory and periodic solutions of impulsive differential equations with piecewise constant argument, Acta Appl. Math., 110 (2010), 499-510.
doi: 10.1007/s10440-009-9458-9. |
[4] |
J. Diblík, A note on explicit criteria for the existence of positive solutions to the linear advanced equation $\dot x(t) = c(t)x(t + \tau)$, Appl. Math. Lett., 35 (2014), 72-76.
doi: 10.1016/j.aml.2013.11.010. |
[5] |
J. Diblík and N. Koksch, Positive solutions of the equation $\dotx(t)=-c(t)x(t-\tau )$ in the critical case, J. Math. Anal. Appl., 250 (2000), 635-659.
doi: 10.1006/jmaa.2000.7008. |
[6] |
J. Diblík and M. Kúdelčíková, Positive solutions of advanced differential systems, The Scientific World Journal, 2013 (2013), Article ID 613832, 1-7.
doi: 10.1155/2013/613832. |
[7] |
A. Domoshnitsky and M. Drakhlin, Nonoscillation of first order differential equations with delay, J. Math. Anal. Appl., 206 (1997), 254-269.
doi: 10.1006/jmaa.1997.5231. |
[8] |
Y. Domshlak and I. P. Stavroulakis, Oscillation of first-order delay differential equations in a critical case, Appl. Anal., 61 (1996), 359-371.
doi: 10.1080/00036819608840464. |
[9] |
B. Dorociaková, M. Kubjatková and R. Olach, Existence of positive solutions of neutral differential equations, Abstr. Appl. Anal., 2012 (2012), Art. ID 307968, 14 pp.
doi: 10.1155/2012/307968. |
[10] |
Á. Elbert and I. P. Stavroulakis, Oscillation and non-oscillation criteria for delay differential equations, Proc. Amer. Math. Soc., 123 (1995), 1503-1510.
doi: 10.1090/S0002-9939-1995-1242082-1. |
[11] |
L. H. Erbe, Q. Kong and B. G. Zhang, Oscillation Theory for Functional Differential Equations, Marcel Dekker, New York, Basel, Hong Kong, 1994. |
[12] |
I. Györi and G. Ladas, Oscillation Theory of Delay Differential Equations, Clarendon Press, 1991. |
[13] |
V. E. Sljusarchuk, The necessary and sufficient conditions for oscillation of solutions of nonlinear differential equations with pulse influence in the Banach space, Ukrain. Mat. Zh., 51 (1999), 98-109.
doi: 10.1007/BF02591918. |
[14] |
B. G. Zhang, Oscillation of the solutions of the first-order advanced type differential equations, (Chinese summary), Sci. Exploration, 2 (1982), 79-82. |
show all references
References:
[1] |
R. P. Agarwal, L. Berezansky, E. Braverman and A. Domoshnitsky, Nonoscillation Theory of Functional Differential Equations with Applications, Springer, 2012.
doi: 10.1007/978-1-4614-3455-9. |
[2] |
R. P. Agarwal, M. Bohner and W.-T. Li, Nonoscillation and Oscillation: Theory for Functional Differential Equations, Marcel Dekker, Inc., 2004.
doi: 10.1201/9780203025741. |
[3] |
H. Bereketoǧlu, F. Karakoç and G. Seyhan, Oscillatory and periodic solutions of impulsive differential equations with piecewise constant argument, Acta Appl. Math., 110 (2010), 499-510.
doi: 10.1007/s10440-009-9458-9. |
[4] |
J. Diblík, A note on explicit criteria for the existence of positive solutions to the linear advanced equation $\dot x(t) = c(t)x(t + \tau)$, Appl. Math. Lett., 35 (2014), 72-76.
doi: 10.1016/j.aml.2013.11.010. |
[5] |
J. Diblík and N. Koksch, Positive solutions of the equation $\dotx(t)=-c(t)x(t-\tau )$ in the critical case, J. Math. Anal. Appl., 250 (2000), 635-659.
doi: 10.1006/jmaa.2000.7008. |
[6] |
J. Diblík and M. Kúdelčíková, Positive solutions of advanced differential systems, The Scientific World Journal, 2013 (2013), Article ID 613832, 1-7.
doi: 10.1155/2013/613832. |
[7] |
A. Domoshnitsky and M. Drakhlin, Nonoscillation of first order differential equations with delay, J. Math. Anal. Appl., 206 (1997), 254-269.
doi: 10.1006/jmaa.1997.5231. |
[8] |
Y. Domshlak and I. P. Stavroulakis, Oscillation of first-order delay differential equations in a critical case, Appl. Anal., 61 (1996), 359-371.
doi: 10.1080/00036819608840464. |
[9] |
B. Dorociaková, M. Kubjatková and R. Olach, Existence of positive solutions of neutral differential equations, Abstr. Appl. Anal., 2012 (2012), Art. ID 307968, 14 pp.
doi: 10.1155/2012/307968. |
[10] |
Á. Elbert and I. P. Stavroulakis, Oscillation and non-oscillation criteria for delay differential equations, Proc. Amer. Math. Soc., 123 (1995), 1503-1510.
doi: 10.1090/S0002-9939-1995-1242082-1. |
[11] |
L. H. Erbe, Q. Kong and B. G. Zhang, Oscillation Theory for Functional Differential Equations, Marcel Dekker, New York, Basel, Hong Kong, 1994. |
[12] |
I. Györi and G. Ladas, Oscillation Theory of Delay Differential Equations, Clarendon Press, 1991. |
[13] |
V. E. Sljusarchuk, The necessary and sufficient conditions for oscillation of solutions of nonlinear differential equations with pulse influence in the Banach space, Ukrain. Mat. Zh., 51 (1999), 98-109.
doi: 10.1007/BF02591918. |
[14] |
B. G. Zhang, Oscillation of the solutions of the first-order advanced type differential equations, (Chinese summary), Sci. Exploration, 2 (1982), 79-82. |
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