Existence and uniqueness of periodic solutions for a kind of Liénard equation with a deviating argument

AbstractIn this work, we use the coincidence degree theory to establish new results on the existence and uniqueness of T-periodic solutions for a kind of Liénard equation with a deviating argument of the form x″(t)+f(x(t))x′(t)+g(t,x(t−τ(t)))=p(t)

Periodic solutions for a generalized p-Laplacian equation

AbstractThe existence and uniqueness of T-periodic solutions for the following boundary value problems with p-Laplacian: (ϕp(x′))′+f(t,x′)+g(t,x)=e(t),x(0)=x(T),x′(0)=x′(T) are investigated, where ϕp(u)=∣u∣p−2u with p>1 and f,g,e are continuous and are T-periodic in t with f(t,0)=0. Using coincidence degree theory, some existence and uniqueness results are presented

Periodic solutions for nonlinear nth order differential equations with delays

AbstractBy applying the continuation theorem of coincidence degree theory, we establish the existence of 2π-periodic solutions for a class of nonlinear nth order differential equations with delays

Boundedness criteria for a class of second order nonlinear differential equations with delay

summary:We consider certain class of second order nonlinear nonautonomous delay differential equations of the form $$a(t)x^{\prime \prime } + b(t)g(x,x^\prime ) + c(t)h(x(t-r))m(x^\prime ) = p(t,x,x^\prime )$$ and $$(a(t)x^\prime )^\prime + b(t)g(x,x^\prime ) + c(t)h(x(t-r))m(x^\prime ) = p(t,x,x^\prime ),$$ where $a$, $b$, $c$, $g$, $h$, $m$ and $p$ are real valued functions which depend at most on the arguments displayed explicitly and $r$ is a positive constant. Different forms of the integral inequality method were used to investigate the boundedness of all solutions and their derivatives. Here, we do not require construction of the Lyapunov-Krasovski\v ı functional to establish our results. This work extends and improve on some results in the literature