Positive periodic solution for prescribed mean curvature generalized Liénard equation with a singularity. (English) Zbl 1495.34064
Summary: The main purpose of this paper is to investigate the existence of a positive periodic solution for a prescribed mean curvature generalized Liénard equation with a singularity (weak and strong singularities of attractive type, or weak and strong singularities of repulsive type). Our proof is based on an extension of Mawhin’s continuation theorem.
MSC:
| 34C25 | Periodic solutions to ordinary differential equations |
| 34B16 | Singular nonlinear boundary value problems for ordinary differential equations |
| 37C60 | Nonautonomous smooth dynamical systems |
| 34A09 | Implicit ordinary differential equations, differential-algebraic equations |
| 34B30 | Special ordinary differential equations (Mathieu, Hill, Bessel, etc.) |
| 47N20 | Applications of operator theory to differential and integral equations |
| 34B18 | Positive solutions to nonlinear boundary value problems for ordinary differential equations |
Keywords:
positive periodic solution; prescribed mean curvature; weak and strong; attractive and repulsive; Liénard equationReferences:
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