Existence of positive solutions for a Neumann boundary value problem on the half-line via coincidence degree

Abstract

AbstractIn this paper, we are interested in the study of the existence of positive solutions for the following nonlinear boundary value problem on the half-line:\left\{\begin{aligned} \displaystyle-u^{\prime\prime}(x)&\displaystyle=q(x)f(x% ,u,u^{\prime}),&&\displaystyle x\in(0,+\infty),\\ \displaystyle u^{\prime}(0)&\displaystyle=u^{\prime}(+\infty)=0,\end{aligned}\right.where {q:\mathbb{R^{+}}\rightarrow\mathbb{R^{+}}} is a positive measurable function such that {\int_{0}^{+\infty}q(x)\,dx=1} and {f:\mathbb{R}^{+}\times\mathbb{R}^{2}\rightarrow\mathbb{R}} is q-Carathéodory.