Approximate controllability of impulsive differential equations with state-dependent delay

References

• Anandhi , ER and Voit , EO . 2005 . Controllability of Non-linear Biochemical Systems . Mathematical Biosciences , 196 : 99 – 123 .
   PubMed Web of Science ®Google Scholar
• Arino , O , Habid , ML and de la Parra , RB . 1998 . A Mathematical Model of Growth of Population of Fish in the Larval Stage: Density-dependence Effects . Mathematical Biosciences , 150 : 1 – 20 .
   PubMed Web of Science ®Google Scholar
• Balasubramaniam , P , Dauer , JP and Loganathan , C . 2002 . Local Controllability of Functional Integrodifferential Equation in Banach Space . Journal of Optimization Theory and Applications , 114 : 273 – 286 .
   Web of Science ®Google Scholar
• Balachandran , K and Sakthivel , R . 2001 . Controllability of Functional Semilinear Integrodifferential Systems in Banach Spaces . Journal of Mathematical Analysis and Applications , 255 : 447 – 457 .
   Web of Science ®Google Scholar
• Ballinger , G and Liu , X . 2003 . Boundness for Impulsive Delay Differential Equations and Applications to Population Growth Models . Nonlinear Analysis , 53 : 1041 – 1062 .
   Web of Science ®Google Scholar
• Benchohra , M , Gorniewicz , L , Ntouyas , SK and Ouahab , A . 2006 . Controllability Results for Nondensely Defined Semilinear Functional Differential Equations . Zeitschrift für Analysis und ihre Anwendungen , 25 : 311 – 325 .
   Web of Science ®Google Scholar
• Chalishajar , DN , George , RK and Nandakumaran , AK . 2007 . Exact Controllability of the Third Order Nonlinear Dispersion Equation . Journal of Mathematical Analysis and Applications , 332 : 1028 – 1044 .
   Web of Science ®Google Scholar
• Chang , YK . 2007 . Controllability of Impulsive Functional Differential Systems with Infinite Delay in Banach Spaces . Chaos, Solitons & Fractals , 33 : 1601 – 1609 .
   Web of Science ®Google Scholar
• Chang , YK , Li , WT and Nieto , JJ . 2007 . Controllability of Evolution Differential Inclusions in Banach Spaces . Nonlinear Analysis , 67 : 623 – 632 .
   Web of Science ®Google Scholar
• Dauer , JP and Mahmudov , NI . 2002 . Approximate Controllability of Semilinear Functional Equations in Hilbert Spaces . Journal of Mathematical Analysis and Applications , 273 : 310 – 327 .
   Web of Science ®Google Scholar
• Gao , S , Chen , L , Nieto , JJ and Torres , A . 2006 . Analysis of a Delayed Epidemic Model with Pulse Vaccination and Saturation Incidence . Vaccine , 24 : 6037 – 6045 .
   PubMed Web of Science ®Google Scholar
• Gao , C , Li , K , Feng , E and Xiu , Z . 2006 . Nonlinear Impulsive System of Fed-batch Culture in Fermentative Production and Its Properties . Chaos Solitons & Fractals , 28 : 271 – 277 .
   Web of Science ®Google Scholar
• Gorniewicz , L , Ntouyas , SK and O'Regan , D . 2005 . Controllability of Semilinear Differential Equations and Inclusions via Semigroup Theory in Banach Spaces . Reports on Mathematical Physics , 56 : 437 – 470 .
   Web of Science ®Google Scholar
• Hernandez , E , Sakthivel , R and Tanaka , SA . 2008 . Existence Results for Impulsive Evolution Differential Equations with State-dependent Delay . Electronic Journal of Differential Equations , 28 : 11
   Google Scholar
• Hino , Y , Murakami , S and Naito , T . 1991 . Functional Differential Equations with Infinite Delay, Lecture Notes in Mathematics , Vol. 1473 , Berlin : Springer-Verlag .
   Google Scholar
• Kartsatos , AC . 2005 . On the Approximate K-controllability of Nonlinear Systems in Banach Spaces . Nonlinear Analysis, Theory Methods & Applications , 62 : 315 – 344 .
   Web of Science ®Google Scholar
• Li , ML , Wang , MS and Zhang , FQ . 2006 . Controllability of Impulsive Functional Differential Systems in Banach Spaces . Chaos, Solitons & Fractals , 29 : 175 – 181 .
   Web of Science ®Google Scholar
• Liu , B . 2005 . Controllability of Impulsive Neutral Functional Differential Inclusions with Infinite Delay . Nonlinear Analysis , 60 : 1533 – 1552 .
   Web of Science ®Google Scholar
• Mahaffy , JM , Belair , J and Mackey , MC . 1998 . Hematopoietic Model with Moving Boundary Condition and State Dependent Delay: Applications in Erythropoiesis . Journal of Theoretical Biology , 190 : 135 – 146 .
   PubMed Web of Science ®Google Scholar
• Mahmudov , NI . 2003 . Approximate Controllability of Semilinear Deterministic and Stochastic Evolution Equations in Abstract Spaces . SIAM Journal on Control and Optimization , 42 : 1604 – 1622 .
   Web of Science ®Google Scholar
• Mahmudov , NI . 2008 . Approximate Controllability of Evolution Systems with Nonlocal Conditions . Nonlinear Analysis , 68 : 536 – 546 .
   Web of Science ®Google Scholar
• Naito , K . 1989 . Approximate Controllability for Trajectories of Semilinear Control Systems . Journal of Optimization Theory and Applications , 60 : 57 – 65 .
   Web of Science ®Google Scholar
• Sakthivel , R , Anthoni , SM and Kim , JH . 2005 . Existence and Controllability Result for Semilinear Evolution Integrodifferential Systems . Mathematical and Computer Modelling , 41 : 1005 – 1011 .
   Google Scholar
• Tang , S and Chen , L . 2002 . Density-dependent Birth Rate, Birth Pulses and Their Population Dynamic Consequences . Journal of Mathematical Biology , 44 : 185 – 199 .
   PubMed Web of Science ®Google Scholar