Abstract
In this paper, we propose a new class of functions called $\mu$-pseudo $\mathcal{S}$-asymptotically periodic function on $\mathbb{R}$ by the measure theory. Furthermore, the existence, uniqueness of $\mu$-pseudo $\mathcal{S}$-asymptotically periodic integral solution to partial neutral functional differential equations with finite delay are investigated. Here we assume that the undelayed part is not necessarily densely defined and satisfies the Hille-Yosida condition.
Reference8 articles.
1. M. Adimy and K. Ezzinbi, Existence and linearized stability for partial neutral functional differential equations, Differential Equations and Dynamical Systems, 7 (4) (1999), 371-417.
2. M. Adimy, K. Ezzinbi and M. Laklach, Spectral decomposition for partial neutral functional differential equations, Canadian Applied Mathematics Quarterly, 9 (9) (2001), 1-34.
3. M. Adimy, A. Elazzouzi and K. Ezzinbi, Bohr-Neugebauer type theoremfor some partial neutral functional differential equations, Nonlinear Analysis, 66 (5) (2007), 1145-1160.
4. M. Adimy, K. Ezzinbi and C. Marquet, Ergodic and weighted pseudo-almost periodic solutions for partial functional differential equations in fading memory spaces, Journal of Applied Mathematics and Computing, $44(1-2)(2014), 147-165$.
5. M. Alia, K. Ezzinbi and S. Fatajou, Exponential dichotomy and pseudo-almost automorphy for partial neutral functional differential equations, Nonlinear Analysis, 71 (5-6) (2009), 2210-2226.