International Journal of Dynamical Systems and Differential Equations http://www.inderscience.com/browse/index.php?journalID=223&year=2011&vol=3&issue=4 Inderscience Publishers Ltd en-uk International Journal of Dynamical Systems and Differential Equations 1752-3583 1752-3591 © 2011 Inderscience Publishers Ltd editor@inderscience.com https://www.inderscience.com/images/files/coverImgs/ijdsde_scoverijdsde.jpg http://www.inderscience.com/browse/index.php?journalID=223&year=2011&vol=3&issue=4 http://www.inderscience.com/link.php?id=42938 In this paper we investigate on local and global existence for some semilinear Schroedinger systems having conservation of the energy and masses. Moreover we presents some blowing up examples for 2 x 2 systems. Semilinear Hamiltonian Schroedinger systems
Luca Fanelli, Sandra Lucente, Eugenio Montefusco
International Journal of Dynamical Systems and Differential Equations, Vol. 3, No. 4 (2011) pp. 401 - 422
In this paper we investigate on local and global existence for some semilinear Schroedinger systems having conservation of the energy and masses. Moreover we presents some blowing up examples for 2 x 2 systems.

]]> 10.1504/IJDSDE.2011.042938 International Journal of Dynamical Systems and Differential Equations, Vol. 3, No. 4 (2011) pp. 401 - 422 Luca Fanelli Sandra Lucente Eugenio Montefusco Departamento de Matematicas, Universidad del Pais Vasco, apartado 644, 48080 Bilbao, Spain. ' Dipartimento di Matematica, Universita degli Studi di Bari, via E. Orabona 2, 70100 Bari, Italy. ' Dipartimento di Matematica, Sapienza Universita di Roma, piazzale A. Moro 5, 00185 Roma, Italy NLS Hamiltonian systems local existence global existence blow-up solution semilinear Schroedinger systems energy conservation. 2011-10-08T23:20:50-05:00 3 4 401 422 2011-10-08T23:20:50-05:00 http://www.inderscience.com/link.php?id=42939 In this work, we study a natural extension of the Linear Quadratic Regulator (LQR) on time scales. Here, we unify and extend the Linear Quadratic Tracker (LQT). We seek to find an affine optimal control that minimises a cost functional associated with a completely observable linear system. We then find an affine optimal control for the fixed final state case in terms of the current state. Finally we include an example in disturbance/rejection modelling. A numerical example is also included. The Linear Quadratic Tracker on time scales
Martin Bohner, Nick Wintz
International Journal of Dynamical Systems and Differential Equations, Vol. 3, No. 4 (2011) pp. 423 - 447
In this work, we study a natural extension of the Linear Quadratic Regulator (LQR) on time scales. Here, we unify and extend the Linear Quadratic Tracker (LQT). We seek to find an affine optimal control that minimises a cost functional associated with a completely observable linear system. We then find an affine optimal control for the fixed final state case in terms of the current state. Finally we include an example in disturbance/rejection modelling. A numerical example is also included.

]]> 10.1504/IJDSDE.2011.042939 International Journal of Dynamical Systems and Differential Equations, Vol. 3, No. 4 (2011) pp. 423 - 447 Martin Bohner Nick Wintz Department of Mathematics and Statistics, Missouri University of Science and Technology, 400 West 12th Street, Rolla, MO 65409-0020, USA. ' Department of Mathematics, Lindenwood University, 209 S. Kingshighway, St. Charles, MO 63301, USA time scales dynamic equations optimal control regulator problem tracking problem cost functional Riccati equation linear quadratic tracker LQT linear quadratic tracker regulator LQR rejection modelling disturbance modelling. 2011-10-08T23:20:50-05:00 3 4 423 447 2011-10-08T23:20:50-05:00 http://www.inderscience.com/link.php?id=42940 We consider the equation <span style="position:relative; top:-5px;left:5px;">•</span><span style="position: relative; top: 0px;left: -5px;margin-left:0px;margin-bottom:10px;">y</span> = Ey, where Ey(t) = f<span style="position:relative; top:-5px;left:5px;">η</span><span style="position: relative; top: 5px;left: -5px;margin-left:0px;margin-bottom:10px;">0</span>d<SUB align=right>τR(t, τ)y(t − τ) (t ≥ 0) with an n × n-matrix-valued function R(t, τ). It is proved that, if for a p ≥ 1, the non-homogeneous equation <span style="position:relative; top:-5px;left:5px;">•</span><span style="position: relative; top: 0px;left: -5px;margin-left:0px;margin-bottom:10px;">x</span> = Ex + f with the zero initial condition, for any f ∈ L<SUP align=right>p</SUP>, has a solution x ∈ L<SUP align=right>p</SUP>, then the considered homogeneous equation is exponentially stable. By that result, sharp stability conditions are derived for vector functional differential equations 'close' to autonomous ones and for equations with small delays. The Lp-version of the generalised Bohl-Perron principle for vector equations with delay
Michael I. Gil'
International Journal of Dynamical Systems and Differential Equations, Vol. 3, No. 4 (2011) pp. 448 - 458
We consider the equation <span style="position:relative; top:-5px;left:5px;">•</span><span style="position: relative; top: 0px;left: -5px;margin-left:0px;margin-bottom:10px;">y</span> = Ey, where Ey(t) = f<span style="position:relative; top:-5px;left:5px;">η</span><span style="position: relative; top: 5px;left: -5px;margin-left:0px;margin-bottom:10px;">0</span>d<SUB align=right>τR(t, τ)y(t − τ) (t ≥ 0) with an n × n-matrix-valued function R(t, τ). It is proved that, if for a p ≥ 1, the non-homogeneous equation <span style="position:relative; top:-5px;left:5px;">•</span><span style="position: relative; top: 0px;left: -5px;margin-left:0px;margin-bottom:10px;">x</span> = Ex + f with the zero initial condition, for any f ∈ L<SUP align=right>p</SUP>, has a solution x ∈ L<SUP align=right>p</SUP>, then the considered homogeneous equation is exponentially stable. By that result, sharp stability conditions are derived for vector functional differential equations 'close' to autonomous ones and for equations with small delays.

]]> 10.1504/IJDSDE.2011.042940 International Journal of Dynamical Systems and Differential Equations, Vol. 3, No. 4 (2011) pp. 448 - 458 Michael I. Gil' Department of Mathematics, Ben Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel functional differential equations linear equations exponential stability Bohl-Perron vector equations delay. 2011-10-08T23:20:50-05:00 3 4 448 458 2011-10-08T23:20:50-05:00 http://www.inderscience.com/link.php?id=42941 This paper deals with the existence and uniqueness of solutions of some classes of partial functional and neutral functional hyperbolic differential equations with state-dependent delay involving the Caputo fractional derivative. Our results will be obtained by using suitable fixed point theorems. Fractional order partial hyperbolic functional differential equations with state-dependent delay
Said Abbas, Mouffak Benchohra, Yong Zhou
International Journal of Dynamical Systems and Differential Equations, Vol. 3, No. 4 (2011) pp. 459 - 490
This paper deals with the existence and uniqueness of solutions of some classes of partial functional and neutral functional hyperbolic differential equations with state-dependent delay involving the Caputo fractional derivative. Our results will be obtained by using suitable fixed point theorems.

]]> 10.1504/IJDSDE.2011.042941 International Journal of Dynamical Systems and Differential Equations, Vol. 3, No. 4 (2011) pp. 459 - 490 Said Abbas Mouffak Benchohra Yong Zhou Laboratoire de Mathematiques, Universite de Saida, B.P. 138, 20000, Saida, Algerie. ' Laboratoire de Mathematiques, Universite de Sidi Bel-Abbes, B.P. 89, 22000, Sidi Bel-Abbes, Algerie. ' Department of Mathematics, Xiangtan University, Hunan 411105, China partial differential equations solution left-sided mixed Riemann-Liouville integral Caputo fractional order derivative state dependent delay fixed point. 2011-10-08T23:20:50-05:00 3 4 459 490 2011-10-08T23:20:50-05:00