Boundary value problems for a class of nonlinear differential equations

Abstract

Summary:In the paper it is shown that each solution $u(r,\alpha)$ ot the initial value problem (2), (3) has a finite limit for $r\rightarrow \infty$, and an asymptotic formula for the nontrivial solution $u(r,\alpha)$ tending to 0 is given. Further, the existence of such a solutions is established by examining the number of zeros of two different solutions $u(r,\bar{\alpha})$, $u(r,\hat{\alpha})$