Abstract We consider a nonlinear parametric Dirichlet problem driven by the (p, q)-Laplacian (double phase problem) with a reaction exhibiting the competing effects of three different terms. A parametric one consisting of the sum of a singular term and of a drift term (convection) and of a nonparametric perturbation which is resonant. Using the frozen variable method and eventually a fixed point argument based on an iterative asymptotic process, we show that the problem has a positive smooth solution.

中文翻译：

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对流共振 (p, q) 方程的正解

摘要 我们考虑由 (p, q)-拉普拉斯算子（双相问题）驱动的非线性参数狄利克雷问题，其反应表现出三个不同项的竞争效应。由奇异项和漂移项（对流）和谐振的非参数扰动之和组成的参数项。使用冻结变量方法和最终基于迭代渐近过程的不动点参数，我们表明该问题具有正平滑解。