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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, \[ q''=-\nabla V(q),q\in\mathbb{R}^n. \] 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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