Abstract
This paper is concerned with the prescribed mean curvature Lienard type p-Laplacian equation with two arguments. By employing Mawhin’s coincidence degree theorem and the analysis techniques, some new existence results of periodic solutions are obtained. We also give an example to illustrate the application of our main results.
Highlights
The study of the periodic solutions of prescribed mean curvature equations has become very active; see [ – ] and the references therein
The Liénard equation, Liénard system, and p-Laplacian equations are studied by many people; see for example [ – ]
By using the theory of coincidence degree, the author obtained some sufficient conditions for the existence and uniqueness of periodic solution in the case of τ (t) =
Summary
1 Introduction Recently, the study of the periodic solutions of prescribed mean curvature equations has become very active; see [ – ] and the references therein. In [ ] Wang studied the following prescribed mean curvature Rayleigh equation with one deviating argument: x (t) φp + x (t) + f t, x (t) + g t, x t – τ (t) = e(t) under the assumptions: f (t, u) ≥ a|u|r, ∀(t, u) ∈ R and By using the theory of coincidence degree, the author obtained some sufficient conditions for the existence and uniqueness of periodic solution in the case of τ (t) = .
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