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Multiple solutions for a nonlinear second order differential equation. (English) Zbl 0724.34021
Consider the periodic BVP \(x''+e \cos t\cdot x''-2e \sin t\cdot x'+\alpha \sin x=4e \sin t,\) \(x(0)=x(2\pi),\quad x'(0)=x'(2\pi),\) which describes for \(0<e<1\) and \(| \alpha | \leq 3\) the motion of a satellite. The author proves that if \(| e| <1\) and \(\alpha\) is an arbitrary real number then this BVP has at least two solutions not differing by a multiple of \(2\pi\).

MSC:
34B15 Nonlinear boundary value problems for ordinary differential equations
34A34 Nonlinear ordinary differential equations and systems, general theory
34C25 Periodic solutions to ordinary differential equations
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