## Connecting orbits for a periodically forced singular planar Newtonian system.(English)Zbl 1271.34051

The authors study the existence and multiplicity of connecting orbits for a certain class of planar singular Newtonian systems $\ddot{q}+V_{q}(t,q)=0, \tag{1}$ i.e., solutions of (1) that emanate from a set $$\mathcal{M}$$ composed of two distinct points and terminate at $$\mathcal{M}$$: $$q(\pm\infty)=\lim_{t\longrightarrow\pm\infty}q(t)\in\mathcal{M}$$ and $$\dot{q}(\pm\infty)=0$$, with a periodic strong force $$V_{q}(t,q)$$, an infinitely deep well of Gordon’s type at one point and two stationary points at which a potential $$V(t,q)$$ achieves a strict global maximum. To this end, they minimize the corresponding action functional over the classes of functions in the Sobolev space $$W^{1,2}_{\mathrm{loc}}(\mathbb{R},\mathbb{R}^{2})$$ that turn a given number of times around the singularity.

### MSC:

 34C37 Homoclinic and heteroclinic solutions to ordinary differential equations 49J27 Existence theories for problems in abstract spaces

### Keywords:

heteroclinic orbits; homoclinic orbits; Newtonian systems
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### References:

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