Weyl-almost periodic and asymptotically Weyl-almost periodic properties of solutions to linear and semilinear abstract Volterra integro-differential equations
Matematičeskie zametki SVFU, Tome 25 (2018) no. 2, pp. 65-84
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The main purpose of paper is to consider Weyl-almost periodic and asymptotically Weyl-almost periodic solutions of linear and semilinear abstract Volterra integro-differential equations. We focus our attention to the investigations of Weyl-almost periodic and asymptotically Weyl-almost periodic properties of both, finite and infinite convolution product, working in the setting of complex Banach spaces. We introduce the class of asymptotically (equi)-Weyl-$p$-almost periodic functions depending on two parametres and prove a composition principle for the class of asymptotically equi-Weyl-$p$-almost periodic functions. Basically, our results are applicable in any situations where the variation of parameters formula takes a role. We provide several new contributions to abstract linear and semilinear Cauchy problems, including equations with the Weyl Liouville fractional derivatives and the Caputo fractional derivatives. We provide some applications of our abstract theoretical results at the end of paper, considering primarily abstract degenerate differential equations, including the famous Poisson heat equation and its fractional analogues.
Keywords:
Weyl-$p$-almost periodic functions, asymptotically Weyl-$p$-almost periodic functions, abstract Volterra integro-differential equations.
@article{SVFU_2018_25_2_a6,
author = {M. Kosti\'c},
title = {Weyl-almost periodic and asymptotically {Weyl-almost} periodic properties of solutions to linear and semilinear abstract {Volterra} integro-differential equations},
journal = {Matemati\v{c}eskie zametki SVFU},
pages = {65--84},
year = {2018},
volume = {25},
number = {2},
language = {en},
url = {http://geodesic.mathdoc.fr/item/SVFU_2018_25_2_a6/}
}
TY - JOUR AU - M. Kostić TI - Weyl-almost periodic and asymptotically Weyl-almost periodic properties of solutions to linear and semilinear abstract Volterra integro-differential equations JO - Matematičeskie zametki SVFU PY - 2018 SP - 65 EP - 84 VL - 25 IS - 2 UR - http://geodesic.mathdoc.fr/item/SVFU_2018_25_2_a6/ LA - en ID - SVFU_2018_25_2_a6 ER -
%0 Journal Article %A M. Kostić %T Weyl-almost periodic and asymptotically Weyl-almost periodic properties of solutions to linear and semilinear abstract Volterra integro-differential equations %J Matematičeskie zametki SVFU %D 2018 %P 65-84 %V 25 %N 2 %U http://geodesic.mathdoc.fr/item/SVFU_2018_25_2_a6/ %G en %F SVFU_2018_25_2_a6
M. Kostić. Weyl-almost periodic and asymptotically Weyl-almost periodic properties of solutions to linear and semilinear abstract Volterra integro-differential equations. Matematičeskie zametki SVFU, Tome 25 (2018) no. 2, pp. 65-84. http://geodesic.mathdoc.fr/item/SVFU_2018_25_2_a6/