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Multiplicity of homoclinic solutions for singular second-order conservative systems. (English) Zbl 0868.34001
Consider a second-order system of differential equations, $$ q''=-\nabla V(q),q\in\bbfR^n. $$ It is assumed that the potential energy $V$ has a unique absolute maximum at 0 and a singular set $S$. Conditions are given under which the system has at least $p$ distinct homoclinic trajectories of 0, where $p$ is the least number of independent multiplicative generators of the group $\pi_1(\bbfR^n\setminus S)$.

MSC:
34-02Research monographs (ordinary differential equations)
34C37Homoclinic and heteroclinic solutions of ODE
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