# Positive periodic solution for p-Laplacian neutral Rayleigh equation with singularity of attractive type

Positive periodic solution for p-Laplacian neutral Rayleigh equation with singularity of... In this paper, we consider a kind of p-Laplacian neutral Rayleigh equation with singularity of attractive type, ( ϕ p ( u ( t ) − c u ( t − δ ) ) ′ ) ′ + f ( t , u ′ ( t ) ) + g ( t , u ( t ) ) = e ( t ) . $$\bigl(\phi_{p} \bigl(u(t)-cu(t-\delta) \bigr)' \bigr)'+f \bigl(t,u'(t) \bigr)+g \bigl(t, u(t) \bigr)=e(t).$$ By applications of an extension of Mawhin’s continuation theorem, sufficient conditions for the existence of periodic solution are established. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Journal of Inequalities and Applications Springer Journals

# Positive periodic solution for p-Laplacian neutral Rayleigh equation with singularity of attractive type

, Volume 2018 (1) – Mar 14, 2018
11 pages

/lp/springer_journal/positive-periodic-solution-for-p-laplacian-neutral-rayleigh-equation-BKZqzB49aS
Publisher
Springer International Publishing
Subject
Mathematics; Analysis; Applications of Mathematics; Mathematics, general
eISSN
1029-242X
D.O.I.
10.1186/s13660-018-1654-6
Publisher site
See Article on Publisher Site

### Abstract

In this paper, we consider a kind of p-Laplacian neutral Rayleigh equation with singularity of attractive type, ( ϕ p ( u ( t ) − c u ( t − δ ) ) ′ ) ′ + f ( t , u ′ ( t ) ) + g ( t , u ( t ) ) = e ( t ) . $$\bigl(\phi_{p} \bigl(u(t)-cu(t-\delta) \bigr)' \bigr)'+f \bigl(t,u'(t) \bigr)+g \bigl(t, u(t) \bigr)=e(t).$$ By applications of an extension of Mawhin’s continuation theorem, sufficient conditions for the existence of periodic solution are established.

### Journal

Journal of Inequalities and ApplicationsSpringer Journals

Published: Mar 14, 2018

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