具有消失势的扰动 $$1-$Laplacian 和 $$1-$ 双谐波问题的有界变化解的存在性结果

IF 0.7 Q2 MATHEMATICS Advances in Operator Theory Pub Date : 2024-06-06 DOI:10.1007/s43036-024-00351-8

Mahsa Amoie, Mohsen Alimohammady

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引用次数: 0

摘要

这项工作的重点是研究整个空间 $\mathbb {R}^N$ 中的准线性椭圆问题，该问题涉及 1 拉普拉斯算子和 1 双谐波算子，以及可以在无穷远处消失的势。这项研究是在有界变函数空间内进行的。主要结果是利用不需要 Palais-Smale 条件的山口定理版本证明的。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Existence result of bounded variation solution for a perturbed $1-$Laplacian and $1-$biharmonic problem with vanishing potentials

This work focuses on the investigation of a quasilinear elliptic problem in the entire space $\mathbb {R}^N$, which involves the 1-Laplacian and 1-biharmonic operators, as well as potentials that can vanish at infinity. This research is conducted within the space of functions with bounded variation. The main result is proven using a version of the mountain pass theorem that does not require the Palais-Smale condition.

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