Positive periodic solution for higher-order p-Laplacian neutral singular Rayleigh equation with variable coefficient

In this paper, we consider the existence of a positive periodic solution for the following kind of high-order p -Laplacian neutral singular Rayleigh equation with variable coefficient: ( φ p ( x ( t ) − c ( t ) x ( t − σ ) ) ( n ) ) ( m ) + f ( t , x ′ ( t ) ) + g ( t , x ( t ) ) = e ( t ) . Our pro...

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Bibliographic Details
Published inBoundary value problems Vol. 2017; no. 1; pp. 1 - 14
Main Authors Xin, Yun, Yao, Shaowen, Cheng, Zhibo
Format Journal Article
LanguageEnglish
Published Cham Springer International Publishing 19.10.2017
Hindawi Limited
SpringerOpen
Subjects
Analysis
Approximations and Expansions
Difference and Functional Equations
high-order
Mathematics
Mathematics and Statistics
neutral operator
Ordinary Differential Equations
Partial Differential Equations
periodic solution
singularity
variable coefficient
periodic solution
34K40
variable coefficient
34C25
high-order
singularity
34K13
neutral operator
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Summary:In this paper, we consider the existence of a positive periodic solution for the following kind of high-order p -Laplacian neutral singular Rayleigh equation with variable coefficient: ( φ p ( x ( t ) − c ( t ) x ( t − σ ) ) ( n ) ) ( m ) + f ( t , x ′ ( t ) ) + g ( t , x ( t ) ) = e ( t ) . Our proof is based on Mawhin’s continuation theory.
ISSN:1687-2770
1687-2762
1687-2770
DOI:10.1186/s13661-017-0883-9