Periodic solutions of damped differential systems with repulsive singular forces
Periodic solutions of damped differential systems with repulsive singular forces
We consider the periodic boundary value problem for the singular differential system: $u''+(\nabla F(u))â+\nabla G(u) = h(t),$ where $F\in C^{2}(\mathbb R ^{N}, \mathbb R )$, $G\in C^{1}(\mathbb R ^{N} \backslash \{0\}, \mathbb R )$, and $h\in L^{1}([0,T], \mathbb R ^{N})$. The singular potential $G(u)$ is of repulsive type in the …