Affiliation:
1. Department of Mathematics, College of Sciences, King Saud University, Riyadh 11451, Saudi Arabia
Abstract
This study looks closely into the analysis of the variation of constants formula given by Φ(t)=S(t)Φ(0)+∫0tS(t−σ)F(σ,Φ(σ))dσ, for t∈[0,T],T>0, within the context of modular function spaces Lρ. Additionally, this research explores practical applications of the variation of constants formula in variable exponent Lebesgue spaces Lp(·). Specifically, the study examines these spaces under certain conditions applied to the exponent function p(·) and the functions F as well as the semigroup S(t), utilizing the symmetry properties of the algebraic semigroup. This investigation sheds light on the intricate interplay between parameters and functions within these mathematical frameworks, offering valuable insights into their behavior and properties in Lp(·).
Funder
King Saud University, Riyadh Saudi Arabia
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