Abstract
In this paper, by using the concept of changing-periodic time scales and composition theorem of time scales introduced in 2015, we establish a local phase space for functional dynamic equations with infinite delay (FDEID) on an arbitrary time scale with a bounded graininess function μ. Through Krasnoseľskiĭ’s fixed point theorem, some sufficient conditions for the existence of local-periodic solutions for FDEID are established for the first time. This research indicates that one can extract a local-periodic solution for dynamic equations on an arbitrary time scale with a bounded graininess function μ through some index function.
This work was done while Chao Wang was a visiting scholar at Texas A&M University-Kingsville. This work is supported by Youth Fund of NSFC (No. 11601470), Tian Yuan Fund of NSFC (No. 11526181), Yunnan Province Science and Technology Department Applied Basic Research Project of China (No. 2014FB102) and Dong Lu Youth Excellent Teachers Development Program of Yunnan University (No. wx069051).
(Communicated by Michal Fečkan)
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© 2018 Mathematical Institute Slovak Academy of Sciences
Articles in the same Issue
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- An extension of F. Šik’s theorem on modular lattices
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Articles in the same Issue
- Idempotents, group membership and their applications
- Residuation in non-associative MV-algebras
- An extension of F. Šik’s theorem on modular lattices
- Weak pseudo-BCK algebras
- Witt functor of a quadratic order
- A modification of a problem of Diophantus
- Cauchy problems involving a Hadamard-type fractional derivative
- Caratheodory’s solution of the Cauchy problem and a question of Z. Grande
- Sturm-Picone comparison theorems for nonlinear impulsive differential equations
- On oscillatory fourth order nonlinear neutral differential equations – III
- Local-periodic solutions for functional dynamic equations with infinite delay on changing-periodic time scales
- On the representation of involutive Jamesian functions
- Refinements of the heinz inequalities for operators and matrices
- Generalizations of Reid inequality
- Probabilistic convergence transformation groups
- Cluster sets and topology
- Some characterizations for Markov processes as mixed renewal processes
- Equivalent conditions of complete convergence for weighted sums of ANA random variables