Abstract The paper deals with a quasilinear Dirichlet problem involving a competing (p,q)-Laplacian and a convection term. Due to the lack of ellipticity, monotonicity and variational structure, the known methods to find a weak solution are not applicable. We develop an approximation procedure permitting to establish the existence of solutions in a generalized sense. If in place of competing (p,q)-Laplacian we consider the usual (p,q)-Laplacian, our results ensure the existence of weak solutions.

中文翻译：

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具有竞争算子和对流的拟线性狄利克雷问题

摘要 本文讨论了一个拟线性 Dirichlet 问题，该问题涉及一个竞争的 (p,q)-Laplacian 和一个对流项。由于缺乏椭圆性、单调性和变分结构，已知的求弱解的方法不适用。我们开发了一个近似程序，允许建立广义意义上的解的存在。如果我们考虑通常的 (p,q)-Laplacian 代替竞争 (p,q)-Laplacian，我们的结果确保弱解的存在。