Homoclinics for second order conservative systems. (English) Zbl 0804.34046

Miranda, Mario (ed.), Partial differential equations and related subjects. Proceedings of the conference dedicated to Louis Nirenberg held in Trento, Italy, September 3-8, 1990. Harlow: Longman Scientific & Technical. Pitman Res. Notes Math. Ser. 269, 21-37 (1992).
The authors consider a conservative system \(q''+ V_ q(q)=0\), \(q\in \mathbb{R}^ n\). It is assumed that the origin is an equilibrium. Usually to prove existence of homoclinic orbits of 0 “superquadraticity” or convexity of the nonlinear part of the vectorfield is assumed. The authors obtain an existence result for homoclinics dropping such a global condition. They also consider singular potentials.
For the entire collection see [Zbl 0785.00033].


34C37 Homoclinic and heteroclinic solutions to ordinary differential equations