On the Bounded Solutions of Volterra Equations

References

• Amerio L Prouse G 1971 Almost Periodic Functions and Functional Equations, Van Nostrand Reinhold New York
   Google Scholar
• Arendt , W and Batty , CJK . 1997 . Almost periodic solutions of first and second oder Cauchy problems . J. Differential Equations , 137 ( 2 ) : 363 – 383 .
   Web of Science ®Google Scholar
• Arendt W Räbiger F Sourour A 1994 Spectral properties of the operators equations AX + XB = Y Quart. J. Math Oxford 2 45 133 149
   Google Scholar
• Burton T 1983 Volterra Integral and Differential Equations Mathematics in Science and Engineering 167 Academic Press, Inc Orlando FL
   Google Scholar
• Chill R 1998 Fourier Transforms and Asymptotics of Evolution Equations PhD dissertation University of Ulm
   Google Scholar
• Cushing , JM . 1976 . Bounded solutions of perturbed Volterra integrodifferential systems . J. Differential Equations , 20 ( 1 ) : 61 – 70 .
   Google Scholar
• Cushing JM 1977 Integrodifferential Equations and Delay Models in Population Dynamics Lecture Notes in Biomathematics 20 Springer-Verlag Berlin
   Google Scholar
• Da Prato G Lunardi A 1986 Periodic solutions for linear integrodifferential equations with infinite delay in Banach spaces In: Favini and Obrecht Eds. Differential Equations in Banach Spaces Lecture Notes in Math 1223 49 60 Springer Verlag Berlin
   Google Scholar
• Fink AM 1974 Almost Periodic Differential Equations Lecture Notes in Math. 377 Springer Verlag Berlin
   Google Scholar
• Gripenberg G Londen SO Staffans O 1990 Volterra Integral and Functional Equations Encyclopedia of Mathematics and its Applications 34 Cambridge University Press Cambridge, New York
   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
• 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, Moscow Univ. Publ. House 1978. English translation by Cambridge University Press
   Google Scholar
• Mallet-Paret , J . 1999 . The global structure of traveling waves in spatially discrete dynamical systems . J. Dynam. Differential Equations , 11 ( 1 ) : 49 – 127 .
   Google Scholar
• Mallet-Paret , J . 1999 . The Fredholm alternative for functional-differential equations of mixed type . J. Dynam. Differential Equations , 11 ( 1 ) : 1 – 47 .
   Google Scholar
• Murakami , S , Naito , T and Minh , NV . 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 and Minh , NV . 1999 . Evolution semigroups and spectral criteria for almost periodic solutions of periodic evolution equations . J. Differential Equations , 152 : 358 – 376 .
   Google Scholar
• Pazy A 1983 Semigroups of linear operators and applications to partial differential equations Applied Math. Sci. 44 Springer-Verlag Berlin-New York
   Google Scholar
• Prüss , J . 1988 . Bounded solutions of Volterra equations . SIAM J. Math. Anal. , 19 : 133 – 149 .
   Google Scholar
• Prüss J 1993 Evolutionary Integral Equations and Applications Birkhäuser Basel
   Google Scholar
• Staffans , O . 1993 . Periodic L 2-solutions of an integrodifferential equation in a Hilbert space . Proc. Amer. Math. Soc. , 117 ( 3 ) : 745 – 751 .
   Google Scholar
• Staffans , O . 1981 . On asymptotically almost periodic solutions of a convolution equation . Trans. Amer. Math. Soc. , 266 ( 2 ) : 603 – 616 .
   Google Scholar
• Vu , QP . 1994 . Almost periodic solutions of Volterra equations . Diff. Int. Eq. , 7 : 1083 – 1093 .
   Google Scholar
• Vu , QP and Schüler , E . 1998 . The operator equation AX-XB = C, stability and asymptotic behaviour of differential equations . J. Differential Equations , 145 : 394 – 419 .
   Web of Science ®Google Scholar
• Wu J 1996 Theory and Applications of Partial Functional Differential Equations, Applied Math. Sci. 119 Springer Berlin-New york
   Google Scholar
• Yoshizawa T 1975 Stability Theory and the Existence of Periodic Solutions and Almost Periodic Solutions, Applied Math. Sciences 14 Springer-Verlag New York
   Google Scholar