Investigation of particlelike solutions in some models of nonlinear physics

A boundary value problem for a nonlinear ordinary differential equation with singularity, which appears in some problems of elementary particle physics is considered. A question about the existence of positive particlelike solutions and particlelike solutions with an infinite sequence of knots by methods of qualitative theory for ordinary differential equations is studied. It is proved that there are particlelike solutions for a wide class of right parts of equation in case, when a function which is in the right part of equation vanishes in zero. Sufficient conditions are presented for the existence of particlelike solution without knots in case when the right part of equation is increasing in zero