Massera criterion for abstract functional differential equations with advance and delay

References

• Arendt W Batty CJK Hieber M Neubrander F 2001 Vector-Valued Laplace Transforms and Cauchy Problems, Birkhäser Basel-Boston-Berlin
   Google Scholar
• Chow , SN and Hale , JK . 1974 . Strongly limit-compact maps . Funkc. Ekvac. , 17 : 31 – 38 .
   Google Scholar
• Furumochi , T , Naito , T and Nguyen Van , Minh . 2002 . Boundedness and almost periodicity of solutions of partial functional differential equations . J. Differential Equations , 180 : 125 – 152 .
   Google Scholar
• Gyori , I and Krisztin , T . 1993 . Oscillation results for linear autonomous partial delay differential equations . J. Math. Anal. Appl. , 174 ( 1 ) : 204 – 217 .
   Google Scholar
• Hatvani , L and Krisztin , T . 1992 . On the existence of periodic solutions for linear inhomogeneous and quasilinear functional differential equations . J. Differential Equations , 97 : 1 – 15 .
   Google Scholar
• Hino Y Murakami S 1987 Periodic solutions of a linear Volterra system. Differential Equations (Xanthi, 1987) Lecture Notes in Pure and Appl. Math 118 319 326 Dekker New York
   Google Scholar
• Hino Y Naito T Nguyen Van Minh Shin JS 2002 Almost Periodic Solutions of Differential Equations in Banach Spaces, Taylor and Francis London-New York
   Google Scholar
• Langenhop , C . 1985 . Periodic and almost periodic solutions of Volterra integral differential equations with infinite memory . J. Differential Equations , 58 : 391 – 403 .
   Web of Science ®Google Scholar
• Levitan BM Zhikov VV 1982 Almost Periodic Functions and Differential Equations, Cambridge University Press, Cambridge London, New York, New Rochelle, Melbourne, Sydney
   Google Scholar
• Li , Y , Lin , Z and Li , Z . 1996 . A Massera type criterion for linear functional differential equations with advanced and delay . J. Math. Anal. Appl. , 200 : 715 – 725 .
   Google Scholar
• Li , Y , Cong , F , Lin , Z and Liu , W . 1999 . Periodic solutions for evolution equations . Nonlinear Anal. , 36 : 275 – 293 .
   Google Scholar
• Massera , JL . 1952 . The existence of periodic solutions of systems of differential equations . Duke Math. J. , 17 : 457 – 475 .
   Google Scholar
• Murakami , S , Naito , T and Nguyen Van , Minh . 2000 . Evolution semigroups and sums of commuting operators: a new approach to the admissibility theory of function spaces . J. Differential Equations , 164 : 240 – 285 .
   Web of Science ®Google Scholar
• Naito , T , Nguyen Van , Minh , Miyazaki , R and Shin , JS . 2000 . A decomposition theorem for bounded solutions and the existence of periodic solutions to periodic differential equations . J. Differential Equations , 160 : 263 – 282 .
   Google Scholar
• Naito , T , Nguyen Van , Minh and Shin , JS . 2001 . New spectral criteria for almost periodic solutions of evolution equations . Studia Mathematica , 145 : 97 – 111 .
   Google Scholar
• Naito , T , Nguyen Van , Minh and Liu , JH . 2003 . On the bounded solutions of Volterra equations . Journal of Mathematical Analysis and Applications , 286 : 705 – 712 .
   Google Scholar
• Nishikawa T Nguyen Van Minh Naito T On the asymptotic periodic solutions of abstract functional differential equations Funkcial Ekvac. to appear
   Google Scholar
• Pazy A 1983 Semigroups of linear operators and applications to partial differential equations Applied Math. Sci 44 Springer-Verlag Berlin
   Google Scholar
• Prüss J 1993 Evolutionary Integral Equations and Applications, Birkhäuser Basel
   Google Scholar
• Shin , JS and Naito , T . 1999 . Semi-Fredholm operators and periodic solutions for linear functional differential equations . J. Differential Equations , 153 : 407 – 441 .
   Google Scholar
• Travis , CC and Webb , GF . 1974 . Existence and stability for partial functional differential equations . Trans. Amer. Math. Soc. , 200 : 394 – 418 .
   Google Scholar