Periodic-solutions of Some Lienard Equations With Singularities
Periodic-solutions of Some Lienard Equations With Singularities
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DOI：
10.1090/s0002-9939-1990-1009991-5
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发表时间：
1990-04
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影响因子：
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通讯作者：
P. Habets;L. Sanchez
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文献类型：
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作者：
P. Habets;L. Sanchez
我们考虑受迫的李纳德方程\(u'' + f(u)u' + g(t, u) = h(t)\)以及边界条件\(u(0) = u(T)\)，\(u'(0) = u'(T)\)，其中\(g\)在\(R\times(0, +\infty)\)上连续且在\(u = 0\)处趋于无穷。我们既考虑经典解，也考虑可能进入奇点\(u = 0\)的广义解。所采用的方法使用上下解和度理论。
We consider the forced Liénard equation u" +f(u)u +g(t, u) = h(l) together with the boundary conditions u(0) = u(T), u'(0) = u'(T), where g is continuous on R x (0, +oo) 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.