## Multiplicity of homoclinic solutions for singular second-order conservative systems.(English)Zbl 0868.34001

Consider a second-order system of differential equations, $q''=-\nabla V(q),q\in\mathbb{R}^n.$ 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 $$\pi_1(\mathbb{R}^n\setminus S)$$.

### MSC:

 34-02 Research exposition (monographs, survey articles) pertaining to ordinary differential equations 34C37 Homoclinic and heteroclinic solutions to ordinary differential equations
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### References:

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