Homoclinic solutions for a class of second-order singular Hamiltonian systems

We consider a class of singular second-order Hamiltonian systems in R-N (N >= 2) q<spacing diaeresis> + del V(q) = 0, q(t) is not an element of D, where V : R-N \ D -> R has a strict global maximum 0 at the origin and D subset of R-N \ {0} is a set of singularities, that is, V(q) -> -infinity as dist(q, D) -> 0. Under the condition that D is a compact set with C-2-boundary and V(q) similar to -[dist(q, D)](-alpha) as dist(q, D) -> 0 for some alpha > 0, we show the existence of a nontrivial homoclinic solution at 0 via a suitable approximation method. (c) 2025 Elsevier Inc. All rights are reserved, including those for text and data mining, AI training, and similar technologies.