Dans cette Note on introduit une nouvelle classe de fonctions que nous appelerons fonctions pseudo presque périodiques avec poids, lesquelles généralisent de façon naturelle les fonctions pseudo presque périodiques que C. Zhang avait introduit dans la littérature il y a une dizaine d'années. Les propriétés de telles fonctions sont étudiées, en particulier, un résultat sur la composition de fonctions pseudo presque périodiques avec poids est obtenu, lequel sert de support lorsqu'on étudie les solutions pseudo presque périodiques avec poids de certaines équations différentielles ou équations aux dérivées partielles sémi-linéaires.
This Note introduces a new class of functions called weighted pseudo almost periodic functions, which generalize in a natural fashion the classical pseudo almost periodic functions due to C. Zhang. Properties of those weighted pseudo almost periodic functions are discussed including a composition result of weighted pseudo almost periodic functions, which plays a crucial role for the solvability of some weighted pseudo almost periodic semilinear differential and partial differential equations.
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@article{CRMATH_2006__343_10_643_0, author = {Diagana, Toka}, title = {Weighted pseudo almost periodic functions and applications}, journal = {Comptes Rendus. Math\'ematique}, pages = {643--646}, publisher = {Elsevier}, volume = {343}, number = {10}, year = {2006}, doi = {10.1016/j.crma.2006.10.008}, language = {en}, url = {http://www.numdam.org/articles/10.1016/j.crma.2006.10.008/} }
TY - JOUR AU - Diagana, Toka TI - Weighted pseudo almost periodic functions and applications JO - Comptes Rendus. Mathématique PY - 2006 SP - 643 EP - 646 VL - 343 IS - 10 PB - Elsevier UR - http://www.numdam.org/articles/10.1016/j.crma.2006.10.008/ DO - 10.1016/j.crma.2006.10.008 LA - en ID - CRMATH_2006__343_10_643_0 ER -
%0 Journal Article %A Diagana, Toka %T Weighted pseudo almost periodic functions and applications %J Comptes Rendus. Mathématique %D 2006 %P 643-646 %V 343 %N 10 %I Elsevier %U http://www.numdam.org/articles/10.1016/j.crma.2006.10.008/ %R 10.1016/j.crma.2006.10.008 %G en %F CRMATH_2006__343_10_643_0
Diagana, Toka. Weighted pseudo almost periodic functions and applications. Comptes Rendus. Mathématique, Tome 343 (2006) no. 10, pp. 643-646. doi : 10.1016/j.crma.2006.10.008. http://www.numdam.org/articles/10.1016/j.crma.2006.10.008/
[1] Composition of pseudo-almost periodic functions and Cauchy problems with operator of nondense domain, Ann. Math. Blaise Pascal, Volume 6 (1999) no. 1, pp. 1-11
[2] Pseudo almost periodic solutions to some differential equations, Nonlinear Anal., Volume 60 (2005) no. 7, pp. 1277-1286
[3] T. Diagana, E. Hernàndez M., Existence and uniqueness of pseudo almost periodic solutions to some abstract partial neutral functional-differential equations and applications, J. Math. Anal. Appl. (2006), in press
[4] T. Diagana, Existence and uniqueness of pseudo almost periodic solutions to some classes of partial evolution equations, Nonlinear Anal. (2005), in press
[5] Pseudo almost periodic solutions of some differential equations, J. Math. Anal. Appl., Volume 181 (1994) no. 1, pp. 62-76
[6] Pseudo almost periodic solutions of some differential equations. II, J. Math. Anal. Appl., Volume 192 (1995) no. 2, pp. 543-561
[7] Integration of vector-valued pseudo almost periodic functions, Proc. Amer. Math. Soc., Volume 121 (1994) no. 1, pp. 167-174
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