Abstract
Sufficient conditions are presented for the existence of positive periodic solutions for a third-order nonlinear differential equation with singularity. Besides, an example is given to illustrate the results.MSC:34K13, 34B16, 34B18.
Highlights
In this paper, we consider the following third-order differential equation with singularity:x + f t, x x + h(t, x)x = g(t, x), ( . )where f, h are continuous function and T-periodic about t, h(t, x) ≤, g : [, T]×(, ∞) → R is an L -Carathéodory function, i.e., it is measurable in the first variable and continuous in the second variable, and for every < r < s there exists hr,s ∈ L [, ω] such that |f (t, x(t))| ≤ hr,s for all x ∈ [r, s] and a.e. t ∈ [, ω], f is ω-periodic function about t
The study of singular differential equations began with the paper of Taliaferro
Taliaferro’s work has attracted the attention of many specialists in differential equations and they have contributed to the research of singular differential equations
Summary
We consider the following third-order differential equation with singularity:. Where f , h are continuous function and T-periodic about t, h(t, x) ≤ , g : [ , T]×( , ∞) → R is an L -Carathéodory function, i.e., it is measurable in the first variable and continuous in the second variable, and for every < r < s there exists hr,s ∈ L [ , ω] such that |f (t, x(t))| ≤ hr,s for all x ∈ [r, s] and a.e. t ∈ [ , ω], f is ω-periodic function about t. The study of singular differential equations began with the paper of Taliaferro. In , Taliaferro [ ] discussed the model equation with singularity q(t)
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