Periodic solutions and their conditional stability for partial neutral functional differential equations

Huy, Nguyen Tien; Nguyen, Thi Loan; Vu, Truong V.

doi:10.1007/s00028-019-00511-x

Cited by 2 publications

(2 citation statements)

References 22 publications

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“…The existence of periodic solutions to (1.1), (1.2) and their variants has been of great interest for many authors (cf. [1,3,4,5,7,9,8,11,12,13,14,18,19]). To establish the existence of periodic solutions to (1.2), one of the key steps is to consider first the existence of periodic solutions to the linear equation (1.1).…”

Section: Introductionmentioning

confidence: 99%

Massera type theorems for abstract non-autonomous evolution equations

Zheng,

Ding

2024

ejde

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We establish two fixed point theorems for affine maps in Banach spaces, with weaker assumptions than those in the literature. Then we establish some Massera type results for abstract linear evolution equations without assuming the existence of bounded solutions, which is an indispensable condition in the classical Massera theorem and in the earlier literature. As application, we present an existence result on periodic mild solutions to abstract nonautonomous semilinear evolution equations. For more information see https://ejde.math.txstate.edu/Volumes/2024/35/abstr.html

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Section: Introductionmentioning

confidence: 99%

Massera type theorems for abstract non-autonomous evolution equations

Zheng,

Ding

2024

ejde

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“…In the case of partial neutral functional differential equations, the first result was obtained by Datko [18]. Since then, a wide range of neutral problems have been investigated, such as: Bohr-Neugebauer type theorems in [2], spectral decomposition problems in [5], existence of decay integral solutions in [6], Hopf bifurcation and stability/instability of periodic orbits in [22,23], conditional stability for periodic partial neutral differential equations in [26], partial neutral functional differentialdifference equations on the unit circle in [35], and regularity of solutions under nonlocal conditions in [38].…”

Section: Introductionmentioning

confidence: 99%

Existence and controllability for neutral partial differential inclusions nondenselly defined on a half-line

Anh¹,

Yen²

2023

ejde

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In this article, we study the existence of the integral solution to the neutral functional differential inclusion $${\frac{d}{dt}\mathcal{D}y_t-A\mathcal{D}y_t-Ly_t \in F(t,y_t), \quad\text{for a.e. }t \in J:=[0,\infty),\\ y_0=\phi \in C_E=C([-r,0];E),\quad r>0,}$$ and the controllability of the corresponding neutral inclusion $${\frac{d}{dt}\mathcal{D}y_t-A\mathcal{D}y_t-Ly_t \in F(t,y_t)+Bu(t),\quad \text{for a.e. } t \in J,\\ y_0=\phi \in C_E,}$$ on a half-line via the nonlinear alternative of Leray-Schauder type for contractive multivalued mappings given by Frigon. We illustrate our results with applications to a neutral partial differential inclusion with diffusion, and to a neutral functional partial differential equation with obstacle constrains.

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Periodic solutions and their conditional stability for partial neutral functional differential equations

Cited by 2 publications

References 22 publications

Massera type theorems for abstract non-autonomous evolution equations

Massera type theorems for abstract non-autonomous evolution equations

Existence and controllability for neutral partial differential inclusions nondenselly defined on a half-line

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