Abstract
In this paper, some sufficient conditions on the existence of \(2k\pi\)-periodic solutions for a kind of prescribed mean curvature Rayleigh equations are given. Then the existence of nontrivial homoclinic solutions for prescribed mean curvature Rayleigh equations is obtained.
Highlights
1 Introduction In this paper, we are concerned with the existence of homoclinic solutions for the following prescribed mean curvature Rayleigh equation: x (t)
Various types of prescribed mean equations have been studied widely by some authors in many papers because of their having appeared in some scientific fields, such as differential geometry and physics
Hold, they obtained the existence of homoclinic solutions for ( . )
Summary
We are concerned with the existence of homoclinic solutions for the following prescribed mean curvature Rayleigh equation:. Some results on the existence of solutions for prescribed mean equations were obtained (see [ – ] and references cited therein). +x (t) sufficient conditions on the existence of periodic solutions for In [ ], Liang and Lu investigated the following prescribed mean curvature Duffing equation:. Hold, they obtained the existence of homoclinic solutions for ) and obtain the existence of homoclinic solutions under the more simple and reasonable conditions. ), we seek a limit of a certain sequence of kT-periodic solutions xk(t) for the following equations:. In order to apply Mawhin’s continuation theorem to study the existence of kT-periodic solution of
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