We consider a nonlinear Dirichlet problem driven by a general nonhomogeneous differential operator and with a reaction exhibiting the combined effects of a parametric singular term plus a Carathéodory perturbation $f(z,x,y)$ which is only locally defined in $x \in {\mathbb {R}} $ . Using the frozen variable method, we prove the existence of a positive smooth solution, when the parameter is small.

中文翻译：

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具有奇异和对流项的非线性非齐次Dirichlet问题

我们考虑由一般非齐次微分算子驱动的非线性Dirichlet问题，并且该反应具有参数奇异项加Carathéodory扰动$ f（z，x，y）$的组合效应，后者仅在$ x \ in中定义{\ mathbb {R}} $。使用冻结变量方法，当参数较小时，我们证明存在正光滑解。