New results on the existence of periodic solutions to a p-Laplacian differential equation with a deviating argument (original) (raw)
Related papers
2020
In the last several years, the existence of periodic solutions for functional differential equations have been widely studied and are still being investigated due to their applications in many fields such as physics, mechanics, the engineering technique fields and so on...(see for example [1-2] and the references given therein), especially, the p-laplacian functional differential equations which arises from fluid mechanical and nonlinear elastic mechanical phenomena has received more and more attention for example in paper [3], by using Mawhin’s continuation theorem, the authors have studied the existence of periodic solution for p-Laplacian neutral functional differential equation:
Periodic Solutions of Singular Nonlinear Perturbations of the Ordinary p-Laplacian
Advanced Nonlinear Studies, 2002
Using some recent extensions of upper and lower solutions techniques and continuation theorems to the periodic solutions of quasilinear equations of p-Laplacian type, we prove the existence of positive periodic solutions of equations of the form (|xʹ|p-2xʹ)ʹ + f(x)xʹ + g(x) = h(t) with p > 1, f arbitrary and g singular at 0. This extends results of Lazer and Solimini for the undamped ordinary differential case.
A Note on the Existence of Periodic Solutions of Second Order Non-Linear Differential Equations
American Journal of Mathematics and Statistics, 2012
Bahman Mehri, using Leray-Schauder fixed point continuation method, established the existence of periodic solutions to equations of the form, x // +(k+h(x)) x / + f(t, x) = p(t),where h is a continuous function, f, p are continuous functions in their respective arguments and periodic with respect to t of period ω and k is a constant.The aim of this research is to extend this result to a wider class of equations of the form, x // +(k+h(x)) x / + F(t, x, x /) = p(t),where F is continuous in t,x and x / ; and periodic with respect to t of period ω and k is a constant, using Leray-Schauder fixed point continuation method.
Multiple nontrivial solutions for nonlinear periodic problems with the p-Laplacian
Journal of Differential Equations, 2007
We consider a nonlinear periodic problem driven by the scalar p-Laplacian with a nonsmooth potential (hemivariational inequality). Using the degree theory for multivalued perturbations of (S) + -operators and the spectrum of a class of weighted eigenvalue problems for the scalar p-Laplacian, we prove the existence of at least three distinct nontrivial solutions, two of which have constant sign.