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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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