Abstract
The main purpose of this paper is to obtain an exact expression of the positive periodic solution for a first-order differential equation with attractive and repulsive singularities. Moreover, we prove the existence of at least one positive periodic solution for this equation with an indefinite singularity by applications of topological degree theorem, and give the upper and lower bounds of the positive periodic solution.
Abstract
This paper is devoted to the existence of a periodic solution for ϕ-Laplacian neutral differential equation as follows
$$\begin{array}{}
(\phi(x(t)-cx(t-\tau))')'=f(t,x(t),x'(t)).
\end{array}$$
By applications of an extension of Mawhin’s continuous theorem due to Ge and Ren, we obtain that given equation has at least one periodic solution. Meanwhile, the approaches to estimate a priori bounds of periodic solutions are different from the corresponding ones of the known literature.
An exact expression of positive periodic solution for a first-order singular equation
