Abstract
The purpose of this paper is to study the nonlinear distributed delay differential equations with impulses effects in the vectorial regulated Banach spaces R ( [ − r , 0 ] , R n ) . The existence of the periodic solution of impulsive delay differential equations is obtained by using the Schäffer fixed point theorem in regulated space R ( [ − r , 0 ] , R n ) .
Highlights
We will investigate the existence of periodic solutions for vectorial distributed delay differential equations with impulses in regulated Banach spaces
Symmetry 2019, 11, 523 differential equations in regulated vectorial space, taking into account the general theory of functional analysis and having an acceptable hypothesis that can be used in real life applications, see [12] for more details
The aim of this paper is to extend the main results related to the existence of the ω-periodic solutions for ordinary differential equations with impulses presented by Li et al [16] and Nieto [17]
Summary
We will investigate the existence of periodic solutions for vectorial distributed delay differential equations with impulses in regulated Banach spaces. Symmetry 2019, 11, 523 differential equations in regulated vectorial space, taking into account the general theory of functional analysis and having an acceptable hypothesis that can be used in real life applications, see [12] for more details. = φ(θ ), θ ∈ [−τ, 0] and x (0+ ) = ξ ∈ Rn. The aim of this paper is to extend the main results related to the existence of the ω-periodic solutions for ordinary differential equations with impulses presented by Li et al [16] and Nieto [17]. These papers contain references which provide additional reading on this topic, i.e., differential equations with impulses by using the fixed point theory
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