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Positive periodic solutions for singular high-order neutral functional differential equations

  • Fanchao Kong EMAIL logo , Zhiguo Luo and Shiping Lu
Published/Copyright: March 31, 2018
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Mathematica Slovaca
From the journal Mathematica Slovaca Volume 68 Issue 2

Abstract

In this paper, we establish new results on the existence of positive periodic solutions for the following high-order neutral functional differential equation (NFDE)

(x(t)−cx(t−σ))(2m)+f(x(t))x′(t)+g(t,x(t−δ))=e(t).

The interesting thing is that g has a strong singularity at x = 0 and satisfies a small force condition at x = ∞, which is different from the corresponding ones known in the literature. Two examples are given to illustrate the effectiveness of our results.

MSC 2010: Primary 34B16; 34K13
Keywords: neutral functional differential equation; positive periodic solutions; high order; singularity

Communicated by Michal Fečkan

Acknowledgement

The authors would like to express their great thanks to the reviewers who carefully reviewed the manuscript. The research was supported by the National Natural Science Foundation of China (Grant No.11471109) and the National Natural Science Foundation of China (Grant No.11271197).

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Received: 2015-9-18
Accepted: 2016-9-26
Published Online: 2018-3-31
Published in Print: 2018-4-25

© 2018 Mathematical Institute Slovak Academy of Sciences

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  6. On lattices of z-ideals of function rings
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  10. Lifting components in clean abelian ℓ-groups
  12. Invariance of nonatomic measures on effect algebras
  14. On the alexander dual of path ideals of cycle posets
  16. Generalized multiplicative derivations in 3-prime near rings
  18. Cleft extensions for quasi-entwining structures
  20. Groups with positive rank gradient and their actions
  22. Certain results on q-starlike and q-convex error functions
  24. Faber polynomial coefficient estimates for subclass of bi-univalent functions defined by quasi-subordinate
  26. Positive periodic solutions for singular high-order neutral functional differential equations
  28. A special class of functional equations
  30. Matrix mappings and general bounded linear operators on the space bv
  32. Skew-symmetric operators and reflexivity
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  38. Suzuki-type of common fixed point theorems in fuzzy metric spaces
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https://doi.org/10.1515/ms-2017-0109
Keywords for this article
neutral functional differential equation; positive periodic solutions; high order; singularity

Articles in the same Issue

  2. On the family of functions with closure of graphs in the Mendez ideals
  4. The predicate completion of a partial information system
  6. On lattices of z-ideals of function rings
  8. Compactifications of partial frames via strongly regular ideals
  10. Lifting components in clean abelian ℓ-groups
  12. Invariance of nonatomic measures on effect algebras
  14. On the alexander dual of path ideals of cycle posets
  16. Generalized multiplicative derivations in 3-prime near rings
  18. Cleft extensions for quasi-entwining structures
  20. Groups with positive rank gradient and their actions
  22. Certain results on q-starlike and q-convex error functions
  24. Faber polynomial coefficient estimates for subclass of bi-univalent functions defined by quasi-subordinate
  26. Positive periodic solutions for singular high-order neutral functional differential equations
  28. A special class of functional equations
  30. Matrix mappings and general bounded linear operators on the space bv
  32. Skew-symmetric operators and reflexivity
  34. Derivatives of Hadamard type in vector optimization
  36. Cardinal functions of the hyperspace of convergent sequences
  38. Suzuki-type of common fixed point theorems in fuzzy metric spaces
  40. Second hankel determinat for certain analytic functions satisfying subordinate condition
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