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Staněk, Svatoslav
Periodic solutions of nonlinear second-order differential equations with parameter. (English). Mathematica Bohemica, vol. 117 (1992), issue 4, pp. 337-348
MSC: 34B15, 34C25 | MR 1197284 | Zbl 0771.34034 | DOI: 10.21136/MB.1992.126060
Keywords:
periodic solution; nonlinear second-order differential equation with a parameter; Schauder fixed point theorem
Summary:
This paper establishes effective sufficient conditions for existence and uniqueness of periodic solutions of a one-parameter differential equation $u''-q(t)y=f(t,y,y',\mu)$ vanishing at an arbitrary but fixed point.
References:
[1] E. F. Beckenbach, R. Bellman: Inequalities. Moscow, 1965. (In Russian.) MR 0192009 | Zbl 0186.09605
[2] S. Staněk: Three-point boundary value problem of nonlinear second order differential equation with parameter. Czechoslovak Math. J. 42(117) (1992), 241-256. MR 1179496
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