Existence results for an impulsive neutral functional differential equation with state-dependent delay

References

• Adimy , M and Ezzinbi , K . 1997 . A class of linear partial neutral functional-differential equations with nondense domain. . Journal of Differential Equations, , 147 ( 2 ) : 285 – 332 .
   Web of Science ®Google Scholar
• Aiello , W , Freedman , HI and Wu , J . 1992 . Analysis of a model representing stage-structured population growth with state-dependent time delay. . SIAM Journal Applied Mathematics, , 52 ( 3 ) : 855 – 869 .
   Web of Science ®Google Scholar
• Alexander , V and Rezounenko , A . 2007 . Partial differential equations with discrete and distributed state-dependent delays. . Journal of Mathematical Analysis and Applications, , 326 ( 2 ) : 1031 – 1045 .
   Web of Science ®Google Scholar
• Arino , O , Boushaba , K and Boussouar , A . 2000 . A mathematical model of the dynamics of the phytoplankton-nutrient system. Spatial heterogeneity in ecological models (Alcala¬ de Henares, 1998). . Nonlinear Analysis RWA , 1 ( 1 ) : 69 – 87 .
   Google Scholar
• Bartha , M . 2003 . Periodic solutions for differential equations with state-dependent delay and positive feedback. . Nonlinear Analysis TMA , 53 ( 6 ) : 839 – 857 .
   Web of Science ®Google Scholar
• Cao , Y , Fan , J and Gard , TC . 1992 . The effects of state-dependent time delay on a stage-structured population growth model. . Nonlinear Analysis TMA, , 19 ( 2 ) : 95 – 105 .
   Web of Science ®Google Scholar
• Domoshnitsky , A , Drakhlin , M and Litsyn , E . 2002 . On equations with delay depending on solution. . Nonlinear Analysis TMA , 49 ( 5 ) : 689 – 701 .
   Web of Science ®Google Scholar
• Driver , RD . 1984 . A neutral system with state-dependent delay. . Journal of Differential Equations , 54 ( 1 ) : 73 – 86 .
   Web of Science ®Google Scholar
• Granas , A and Dugundji , J . 2003 . Fixed Point Theory , New York : Springer-Verlag .
   Google Scholar
• Hale , JK and Kato , J . 1978 . Phase space for retarded equations with infinite delay. . Funckcial. Ekvac. , 21 ( 1 ) : 11 – 41 .
   Google Scholar
• Hale , JK and Lunel , V . 1993 . “ Applied Mathematical Sciences ” . In Introduction to Functional-Differential Equations , Vol. 99 , New York : Springer-Verlag .
   Google Scholar
• Hale , JK . 1994 . Partial neutral functional-differential equations. . Rev. Roumaine Math. Pures Appl. , 39 ( 4 ) : 339 – 344 .
   Google Scholar
• Hartung , F , Herdman , TL and Turi , J . 2000 . Parameter identification in classes of neutral differential equations with state-dependent delays. . Nonlinear Analysis TMA. Ser. A: Theory Methods, , 39 ( 3 ) : 305 – 325 .
   Web of Science ®Google Scholar
• Hartung , F . 2001 . Parameter estimation by quasilinearization in functional differential equations with state-dependent delays: a numerical study; Proceedings of the Third World Congress of Nonlinear Analysis, Part 7 (Catania, 2000); . Nonlinear Analysis TMA , 47 ( 7 ) : 4557 – 4566 .
   Web of Science ®Google Scholar
• Hernández , E and Henríquez , H . 1998 . Existence results for partial neutral functional differential equations with unbounded delay. . Journal of Mathematical Analysis and Applications , 221 ( 2 ) : 452 – 475 .
   Web of Science ®Google Scholar
• Hernández , E and Henríquez , H . 1998 . Existence of periodic solutions of partial neutral functional differential equations with unbounded delay. . Journal of Mathematical Analysis and Applications , 221 ( 2 ) : 499 – 522 .
   Web of Science ®Google Scholar
• Hernández , E . 2004 . Existence results for partial neutral integrodifferential equations with unbounded delay. . Journal of Mathematical Analysis and Applications , 292 ( 1 ) : 194 – 210 .
   Web of Science ®Google Scholar
• Hernández , E and Henríquez , HR . 2006 . Impulsive partial neutral differential equations, . Applied Mathematics Letters , 19 ( 3 ) : 215 – 222 .
   Web of Science ®Google Scholar
• Hernández , E , Henríquez , H and Rabelo , M . Existence of solutions for a class of impulsive partial neutral functional differential equations. . Journal of Mathematical Analysis and Applications , Available on line (In press)
   Google Scholar
• Hernández , E , Pierri , M and Goncalves , G . 2006 . Existence results for an impulsive abstract partial differential equation with state-dependent delay. . Computational and Applied Mathematics , 52 : 411 – 420 .
   Web of Science ®Google Scholar
• Hernández , E and Mckibben , M . 2007 . On state-dependent delay partial neutral functional differential equations. . Applied Mathematics and Computation , 180 2006, No. 1, 294--301, doi: 10.1016/j.amc. 2006.07.103
   Google Scholar
• Hernández , E , Prokopczyk , A and Ladeira , L . 2006 . A note on partial functional differential equations with state-dependent delay. . Nonlinear Analysis: Real World Applications , 7 : 510 – 519 .
   Web of Science ®Google Scholar
• Hino , Y , Murakami , S and Naito , T . 1991 . “ Lecture Notes in Mathematics ” . In Functional-differential equations with infinite delay , Vol. 1473 , Berlin : Springer-Verlag .
   Google Scholar
• Lakshmikantham , V , Bainov , DD and Simeonov , PS . 1989 . Theory of Impulsive Differential Equations , Singapore : World Scientific .
   Google Scholar
• Liu , J and James , H . 1999 . Nonlinear impulsive evolution equations. . Dynamics of Continuous, Discrete & Impulsive Systems , 6 ( 1 ) : 77 – 85 .
   Web of Science ®Google Scholar
• Martin , RH . 1987 . Nonlinear Operators and Differential Equations in Banach Spaces , Florida : Robert E. Krieger Publ. Co. .
   Google Scholar
• Pazy , A . 1983 . “ Applied Mathematical Sciences ” . In Semigroups of Linear Operators and Applications to Partial Differential Equations , Vol. 44 , New York-Berlin : Springer-Verlag .
   Google Scholar
• Rogovchenko , YV . 1997 . Impulsive evolution systems: main results and new trends. . Dynamics of Continuous, Discrete & Impulsive Systems , 3 ( 1 ) : 57 – 88 .
   Web of Science ®Google Scholar
• Rogovchenko , YV . 1997 . Nonlinear impulse evolution systems and applications to population models. . Journal of Mathematical Analysis and Applications , 207 ( 2 ) : 300 – 315 .
   Web of Science ®Google Scholar
• Samoilenko , AM and Perestyuk , NA . 1995 . Impulsive Differential Equations , Singapore : World Scientific .
   Google Scholar
• Wu , J and Xia , H . 1996 . Self-sustained oscillations in a ring array of coupled lossless transmission lines. . Journal of Differential Equations , 124 ( 1 ) : 247 – 278 .
   Web of Science ®Google Scholar
• Wu , J . 1996 . “ Applied Mathematical Sciences ” . In Theory and Applications of Partial Functional-Differential Equations , Vol. 119 , New York : Springer-Verlag . (In press)
   Google Scholar
• Wu , J and Rezounenko , A . 2006 . A non-local PDE model for population dynamics with state-selective delay: Local theory and global attractors. . Journal of Computational and Applied Mathematics , 190 ( 1–2 ) : 99 – 113 . Available on line
   Web of Science ®Google Scholar
• Yang , Z and Cao , J . 2005 . Existence of periodic solutions in neutral state-dependent delays equations and models. . Journal of Computational and Applied Mathematics , 174 ( 1 ) : 179 – 199 .
   Web of Science ®Google Scholar