In the present paper, we consider boundary value problems on the real half-line \({\varLambda }:= [0,\infty )\) of the following form

where \({\varPhi }:{\mathbb {R}}\rightarrow {\mathbb {R}}\) is a strictly increasing homeomorphism, \(a\in C({\varLambda }\times {\mathbb {R}},{\mathbb {R}})\) is nonnegative which can vanish on a set of zero Lebesgue measure and f is a Caratheódory function on \({\varLambda }\times {\mathbb {R}}^2\). Under very general assumptions on the functions a and f, including an appropriate version of the well-known Nagumo–Wintner growth condition, we prove the existence of at least one solution of the above problem in a suitable Sobolev space. Our approach combines a fixed-point technique with the method of lower/upper solutions.

在本文中，我们考虑以下形式的实半线\（{\ varLambda}：= [0，\ infty} \）上的边值问题

其中\（{\ varPhi}：{\ mathbb {R}} \ rightarrow {\ mathbb {R}} \）是严格增加的同胚性，\（a \ in C（{\ varLambda} \ times {\ mathbb {R }}，{\ mathbb {R}}）\）是非负数，可以在一组零Lebesgue测度上消失，而f是\（{\ varLambda} \ times {\ mathbb {R}} ^ 2 \上的Caratheódory函数）。在关于函数a和f的非常笼统的假设（包括著名的Nagumo–Wintner生长条件的适当版本）下，我们证明了在合适的Sobolev空间中至少存在上述问题的一种解决方案。我们的方法将定点技术与较低/较高解决方案的方法结合在一起。