Abstract Let A ( s , t ) be a continuous function with a positive lower bound m, and Ω be a bounded domain in R N . In this short note, we propose an iterative procedure for finding nonnegative solutions of the following Kirchhoff-Carrier type equations { − A ( ‖ u ‖ p , ‖ ∇ u ‖ 2 ) Δ u = g ( x , u ) x ∈ Ω , u = 0 x ∈ ∂ Ω . The main advantage of our procedure is that the convergent proof of the iterative sequence depends only on comparison principle of the Laplace operator instead of comparison principle of Kirchhoff-Carrier type operator itself. Therefore, we almost need no restrictions on A ( s , t ) except for continuous and a positive lower bound. This removes away the monotonicity assumption of A ( s , t ) used in most papers based on sub-supersolution method. As applications of the abstract result obtained by our iterative method, some concrete examples are also studied in Section 2 of this paper.

中文翻译：

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Kirchhoff-Carrier型方程的迭代方法及其应用

摘要 设 A ( s , t ) 是一个具有正下界 m 的连续函数，Ω 是 RN 中的一个有界域。在这个简短的说明中，我们提出了一个迭代程序来寻找以下 Kirchhoff-Carrier 类型方程的非负解 { − A ( ‖ u ‖ p , ‖ ∇ u ‖ 2 ) Δ u = g ( x , u ) x ∈ Ω , u = 0 x ∈ ∂ Ω 。我们程序的主要优点是迭代序列的收敛证明仅依赖于拉普拉斯算子的比较原理，而不是基尔霍夫载波类型算子本身的比较原理。因此，除了连续和正下界之外，我们几乎不需要对 A ( s , t ) 进行限制。这消除了大多数基于子超解法的论文中使用的 A ( s , t ) 的单调性假设。作为我们迭代方法获得的抽象结果的应用，