Geodesic
Massera problem for some nonautonomous functional differential equations of neutral type with finite delay
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2022), pp. 61-73

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The paper considers the existence of periodic solutions for some nonautonomous nonlinear partial functional differential equations of neutral type with finite delay. We suppose that the linear part is non-densely defined and satisfies the Acquistapace-Terreni conditions. The delayed part is assumed to be $\omega$-periodic with respect to the first argument. The existence of periodic solutions will be studied in the linear case by using the existence of bounded solutions. In the nonlinear case, a fixed point theorem for multivalued mapping and some sufficient conditions are given to prove the existence of periodic solutions. An example is given to illustrate the theoretical results.
Keywords: Evolution family, mild solution, periodic solutions, fixed point theorem, multivalued map, Poincaré map
Mots-clés : neutral equation. 
@article{IVM_2022_5_a4,
     author = {M. Es-saiydy and I. Oumadane and M. Zitane},
     title = {Massera problem for some nonautonomous functional differential equations of neutral type with finite delay},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {61--73},
     publisher = {mathdoc},
     number = {5},
     year = {2022},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2022_5_a4/}
}
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M. Es-saiydy; I. Oumadane; M. Zitane. Massera problem for some nonautonomous functional differential equations of neutral type with finite delay. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 5 (2022), pp. 61-73. http://geodesic.mathdoc.fr/item/IVM_2022_5_a4/