Periodic solutions for a kind of Liénard equation with two deviating arguments

In this paper, we use the coincidence degree theory to establish new results on the existence of T-periodic solutions for the Liénard equation with two deviating arguments of the form$x^{″}(t)+f(x(t))x^{\prime }(t)+g_1(t,x(t-{\tau }_1(t)))+g_2(t,x(t-{\tau }_2(t)))=p(t)\text{.}$     

Global existence and boundedness for a class of second-order nonlinear differential equations

In this paper we obtain new conditions for the global existence and boundedness of solutions for nonlinear second-order equations of the form ${\left(r\left(t\right){\left|u^{\prime }\right|}^{p?2}{u}^{\prime }\right)}^{\prime }+g(t,u,u^{\prime })u^{\prime }+a\left(t\right)f\left(u\right)=e\left(t\right)\text{,}$ where $p>1$ is a real constant. The results are applicable to well-known Emden–Fowler and Lienard type equations. An illustrative example is also provided.     

Periodic solutions of Liénard equation with a singularity and a deviating argument

In this paper, we study the existence of periodic solutions of the Liénard equation with a singularity and a deviating argument $x^{″}+f\left(x\right)x^{\prime }+g(t,x(t-\sigma ))=0\text{.}$ When $g$ has a strong singularity at $x=0$ and satisfies a new small force condition at $x=\infty$, we prove that the given equation has at least one positive $T$-periodic solution.