Weighted pseudo-almost periodic solutions to some differential equations. (English) Zbl 1131.42006
Summary: The paper considers some new classes of functions called weighted pseudo-almost periodic functions, which implement in a natural fashion the classical pseudo-almost periodic functions due to Zhang. Properties of these weighted pseudo-almost periodic functions are discussed, including a composition result for weighted pseudo-almost periodic functions. The results obtained are subsequently utilized to study the existence and uniqueness of a weighted pseudo-almost periodic solution to the heat equation with Dirichlet conditions.
MSC:
| 42A85 | Convolution, factorization for one variable harmonic analysis |
| 42A75 | Classical almost periodic functions, mean periodic functions |
Keywords:
weight; pseudo-almost periodic; weighted pseudo-almost periodic; almost periodic; heat equationReferences:
| [1] | Ait Dads, E.; Ezzinbi, K.; Arino, O., Pseudo almost periodic solutions for some differential equations in a Banach space, Nonlinear Anal., 28, 7, 1141-1155 (1997) · Zbl 0874.34041 |
| [2] | Ait Dads, E.; Arino, O., Exponential dichotomy and existence of pseudo almost periodic solutions of some differential equations, Nonlinear Anal., 27, 4, 369-386 (1996) · Zbl 0855.34055 |
| [3] | Amir, B.; Maniar, L., Composition of pseudo-almost periodic functions and Cauchy problems with operator of nondense domain, Ann. Math. Blaise Pascal, 6, 1, 1-11 (1999) · Zbl 0941.34059 |
| [4] | Bugajewski, D.; Diagana, T.; Mahop, C. M., Asymptotic and pseudo almost periodicity of the convolution operator and applications to differential and integral equations, J. Anal. Appl., 25, 327-340 (2006) · Zbl 1107.44002 |
| [5] | Corduneanu, C., Almost Periodic Functions (1989), Chelsea: Chelsea New York · Zbl 0672.42008 |
| [6] | Cuevas, C.; Pinto, M., Existence and uniqueness of pseudo almost periodic solutions of semilinear Cauchy problems with non-dense domain, Nonlinear Anal. Ser. A: Theory Methods, 45, 1, 73-83 (2001) · Zbl 0985.34052 |
| [7] | Diagana, T., Weighted pseudo almost periodic functions and applications, C. R. Acad. Sci. Paris, Ser I, 343, 10, 643-646 (2006) · Zbl 1112.43005 |
| [8] | Diagana, T., Pseudo almost periodic solutions to some differential equations, Nonlinear Anal., 60, 7, 1277-1286 (2005) · Zbl 1061.34040 |
| [9] | Diagana, T.; Hernàndez, E. M., Existence and uniqueness of pseudo almost periodic solutions to some abstract partial neutral functional-differential equations and applications, J. Math. Anal. Appl., 327, 2, 776-791 (2007) · Zbl 1123.34060 |
| [10] | Diagana, T.; Mahop, C. M.; N’Guérékata, G. M., Pseudo almost periodic solution to some semilinear differential equations, Math. Comput. Modelling, 43, 1-2, 89-96 (2006) · Zbl 1096.34038 |
| [11] | Diagana, T.; Mahop, C. M.; N’Guérékata, G. M.; Toni, B., Existence and uniqueness of pseudo almost periodic solutions to some classes of semilinear differential equations and applications, Nonlinear Anal., 64, 11, 2442-2453 (2006) · Zbl 1102.34043 |
| [12] | Diagana, T., Existence and uniqueness of pseudo almost periodic solutions to some classes of partial evolution equations, Nonlinear Anal., 66, 2, 384-395 (2007) · Zbl 1105.35304 |
| [13] | Fink, A. M., (Almost Periodic Differential Equations. Almost Periodic Differential Equations, Lecture Notes in Mathematics, vol. 377 (1974), Springer-Verlag: Springer-Verlag New York, Berlin) · Zbl 0325.34039 |
| [14] | Li, H. X.; Huang, F. L.; Li, J. Y., Composition of pseudo almost-periodic functions and semilinear differential equations, J. Math. Anal. Appl., 255, 2, 436-446 (2001) · Zbl 1047.47030 |
| [15] | N’Guérékata, G. M., Almost Automorphic Functions and Almost Periodic Functions in Abstract Spaces (2001), Kluwer Academic/Plenum Publishers: Kluwer Academic/Plenum Publishers New York, London, Moscow · Zbl 1001.43001 |
| [16] | Zhang, C. Y., Pseudo almost periodic solutions of some differential equations, J. Math. Anal. Appl., 181, 1, 62-76 (1994) · Zbl 0796.34029 |
| [17] | Zhang, C. Y., Pseudo almost periodic solutions of some differential equations. II, J. Math. Anal. Appl., 192, 2, 543-561 (1995) · Zbl 0826.34040 |
| [18] | Zhang, C. Y., Integration of vector-valued pseudo almost periodic functions, Proc. Amer. Math. Soc., 121, 1, 167-174 (1994) · Zbl 0818.42003 |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
