Some nonlinear boundary value problems of mixed type on a half line for quasilinear second-order ordinary differential systems

Abstract

Using Leray–Schauder degree, the existence of solutions for quasilinear systems of the form $(q(t)\Phi (x^{\prime }){)}^{\prime }=f(t,x,x^{\prime })$, with nonlinear boundary conditions of mixed type

is proved for various classes of $\Phi$ when $F$ and $f$ satisfy suitable sign conditions.