On the Existence of Periodic Solutions for p-Laplacian Generalized Liénard Equation
نویسندگان
چکیده
By employing Mawhin’s continuation theorem, the existence of periodic solutions of the p-Laplacian generalized Liénard equation with deviating argument (φp(x′(t)))′ + f(t, x(t))x′(t) + β(t)g(x(t− τ(t))) = e(t) under various assumptions are obtained. Keywords—periodic solution, Mawhin’s continuation theorem, deviating argument.
منابع مشابه
Periodic Solutions for p-Laplacian Liénard Equation with a Deviating Argument
By employing Mawhin’s continuation theorem, the existence of periodic solutions of the p-Laplacian Liénard equation with a deviating argument (φp(x′(t)))′ + f(x(t))x′(t) + g(x(t− τ(t))) = e(t) under various assumptions are obtained. Keywords—periodic solution, Mawhin’s continuation theorem, deviating argument.
متن کاملA necessary and sufficient condition for existence and uniqueness of periodic solutions for a p-Laplacian Liénard equation
In this work, we investigate the following p-Laplacian Liénard equation: (φp(x (t))) + f(x(t))x(t) + g(x(t)) = e(t). Under some assumption, a necessary and sufficient condition for the existence and uniqueness of periodic solutions of this equation is given by using Manásevich–Mawhin continuation theorem. Our results improve and extend some known results.
متن کاملUniqueness of Periodic Solution for a Class of Liénard p-Laplacian Equations
Copyright q 2010 Fengjuan Cao et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. By topological degree theory and some analysis skills, we consider a class of generalized Liénard type p-Laplacian equations. Upon some suitable ...
متن کاملExistence of Periodic Solution for Perturbed Generalized Liénard Equations
Under conditions of Levinson-Smith type, we prove the existence of a τ -periodic solution for the perturbed generalized Liénard equation u′′ + φ(u, u′)u′ + ψ(u) = ω( t τ , u, u′) with periodic forcing term. Also we deduce sufficient condition for existence of a periodic solution for the equation
متن کاملEXISTENCE OF PERIODIC SOLUTIONS OF 2α-ORDER NONLINEAR FUNCTIONAL DIFFERENCE EQUATIONS WITH p−LAPLACIAN
The existence of periodic solutions of a higher order nonlinear functional difference equation with p-Laplacian is studied. Sufficient conditions for the existence of periodic solutions of such equation are established. The result is based on Mawhin′s continuation theorem. The methods used to estimate the priori bound on periodic solutions are very technical.
متن کامل