This paper deals with a class of one element n-degree polynomial differential equations. By the fixed point theory, we obtain n periodic solutions of the equation. This paper generalizes some related conclusions of some papers.
In this paper, the concept of a new ?-generalized quasi metric space is
introduced. A number of well-known quasi metric spaces are retrieved from
?-generalized quasi metric space. Some general fixed point theorems in a
?-generalized quasi metric spaces are proved, which generalize, modify and
unify some existing fixed point theorems in the literature. We also give
applications of our results to obtain fixed points for contraction mappings
in the domain of words and to prove the existence of periodic solutions of
delay differential equations.
We present a survey on the existence of periodic solutions of singular differential equations. In particular, we pay our attention to singular scalar differential equations, singular damped differential equations, singular impulsive differential equations, and singular differential systems.
Abstract
We provide sufficient conditions for the existence of periodic solutions of the second-order differential equation with variable potentials
{-(px^{\prime})^{\prime}(t)-r(t)p(t)x^{\prime}(t)+q(t)x(t)=f(t,x(t))}
, where the functions
{p(t)>0}
,
{q(t)}
,
{r(t)}
and
{f(t,x)}
are
{\mathcal{C}^{2}}
and T-periodic in the variable t.
Abstract
This paper deals with the existence of periodic solutions of fractional differential equations with periodic impulses.
The first part of the paper is devoted to the uniqueness, existence and asymptotic stability results for periodic solutions of impulsive fractional differential
equations with varying lower limits for standard nonlinear cases as well as for cases of weak nonlinearities, equidistant and periodically shifted impulses. We also apply our result to an impulsive fractional Lorenz system. The second part extends the study to periodic impulsive fractional differential
equations with fixed lower limit. We show that in general, there are no solutions with long periodic boundary value conditions for the case of bounded nonlinearities.