Irena Rachůnková

Asymptotic Properties of Homoclinic Solutions of Some Singular Nonlinear Differential Equation

abstract:
We investigate an asymptotic behaviour of homoclinic solutions of the singular differential equation $(p(t)u')'=p(t)f(u)$. Here $f$ is Lipschitz continuous on $\mathbb R$ and has at least two zeros $0$ and $L>0$. The function $p$ is continuous on $[0,\infty)$, has a positive continuous derivative on $(0,\infty)$ and $p(0)=0$.

Mathematics Subject Classification: 34D05, 34A12, 34B40

Key words and phrases: Singular ordinary differential equation of the second order, time singularities, asymptotic formula, homoclinic solutions