Periodic solutions of some Liénard equations with singularities
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- by Patrick Habets and Luis Sanchez PDF
- Proc. Amer. Math. Soc. 109 (1990), 1035-1044 Request permission
Abstract:
We consider the forced Liénard equation \[ u'' + f(u)u’ + g(t,u) = h(t)\] together with the boundary conditions \[ u(0) = u(T),\quad u’(0) = u’(T),\] where $g$ is continuous on ${\mathbf {R}} \times (0, + \infty )$ and becomes infinite at $u = 0$. We consider classical solutions as well as generalized solutions that can go into the singularity $u = 0$. The method of approach uses upper and lower solutions and degree theory.References
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Additional Information
- © Copyright 1990 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 109 (1990), 1035-1044
- MSC: Primary 34C25; Secondary 58E05, 58F20
- DOI: https://doi.org/10.1090/S0002-9939-1990-1009991-5
- MathSciNet review: 1009991