533 research outputs found

    Sufficient conditions for the existence of periodic solutions to some second order differential equations with a deviating argument

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    AbstractBy means of Mawhin's continuation theorem, we study some second order differential equations with a deviating argument: x″(t)=f(t,x(t),x(t−τ(t)),x′(t))+e(t). Some new results on the existence of periodic solutions are obtained. The interest is that we allow the degree with respect to the variables x0,x1,x2 of f(t,x0,x1,x2) to be greater than 1; and also the result (Theorem 3.2) is related to the deviating argument τ(t). Meanwhile, we give an example to demonstrate our result

    Uniqueness of Periodic Solution for a Class of Liénard p-Laplacian Equations

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    By topological degree theory and some analysis skills, we consider a class of generalized Liénard type p-Laplacian equations. Upon some suitable assumptions, the existence and uniqueness of periodic solutions for the generalized Liénard type p-Laplacian differential equations are obtained. It is significant that the nonlinear term contains two variables

    Some Results for Periodic Solutions of a Kind of Liénard Equation

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    Periodic solutions for a generalized p-Laplacian equation

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    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

    Antiperiodic Solutions for a Kind of Nonlinear Duffing Equations with a Deviating Argument and Time-Varying Delay

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    This paper deals with a kind of nonlinear Duffing equation with a deviating argument and time-varying delay. By using differential inequality techniques, some very verifiable criteria on the existence and exponential stability of antiperiodic solutions for the equation are obtained. Our results are new and complementary to previously known results. An example is given to illustrate the feasibility and effectiveness of our main results

    On solvability of periodic boundary value problems for second order linear functional differential equations

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    The periodic boundary value problem for second order linear functional differential equations with pointwise restrictions (instead of integral ones) is considered. Sharp sufficient conditions for the solvability are obtained

    Periodicity, Stability, and Boundedness of Solutions to Certain Second Order Delay Differential Equations

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    The behaviour of solutions to certain second order nonlinear delay differential equations with variable deviating arguments is discussed. The main procedure lies in the properties of a complete Lyapunov functional which is used to obtain suitable criteria to guarantee existence of unique solutions that are periodic, uniformly asymptotically stable, and uniformly ultimately bounded. Obtained results are new and also complement related ones that have appeared in the literature. Moreover, examples are given to illustrate the feasibility and correctness of the main results
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