Existence of Solutions for a Nonlocal Boundary Value Problem at Resonance on the Half-Line

In this paper we are interested in the existence of solutions for the following boundary value problem at resonance on the half-line [graphic not available: see fulltext]where f:R+×R2→R\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$f:\mathbb {R}^{+}\times \mathbb {R}^{2}\rightarrow \mathbb {R}$$\end{document} is q-Carathéodory, g:R+→R+\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ g:\mathbb {R}^{+}\rightarrow \mathbb {R}^{+} $$\end{document} is a nondecreasing function with g(0)=0\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g(0)=0$$\end{document} under the resonance condition g(∞)=1\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$g(\infty )= 1$$\end{document}. The coincidence degree theory of Mawhin [17] is used to establish the existence of at least one solution for the posed problem.