Periodic solutions of dissipative dynamical systems with singular potential and $p$-Laplacian
Volume 79 / 2002
Annales Polonici Mathematici 79 (2002), 109-120
MSC: Primary 34C15, 34C25.
DOI: 10.4064/ap79-2-2
Abstract
By using the topological degree theory and some analytic methods, we consider the periodic boundary value problem for the singular dissipative dynamical systems with $p$-Laplacian: $(\phi _p(x'))'+{d\over dt}\mathop {\rm grad}\nolimits F(x)+\mathop {\rm grad}\nolimits G(x)=e(t)$, $x(0)=x(T)$, $x'(0)=x'(T)$. Sufficient conditions to guarantee the existence of solutions are obtained under no restriction on the damping forces ${d\over dt}\mathop {\rm grad}\nolimits F(x)$.
