Existence and nonexistence of solutions for the mean curvature equation with weights

IF 1.3 2区数学 Q1 MATHEMATICS

Mathematische Annalen Pub Date : 2024-05-28 DOI:10.1007/s00208-024-02900-1

Roberta Filippucci, Yadong Zheng

引用次数: 0

Abstract

In this paper we study existence and nonexistence of positive radial solutions of a Dirichlet problem for the prescribed mean curvature operator with weights in a ball with a suitable radius. Because of the presence of different weights, possibly singular or degenerate, the problem under consideration appears rather delicate, it requires an accurate qualitative analysis of the solutions, as well as the use of Liouville type results based on an appropriate Pohozaev type identity. In addition, sufficient conditions for global solutions to be oscillatory are given.

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有权重的平均曲率方程解的存在与不存在

在本文中，我们研究了在一个具有适当半径的球中有权重的规定平均曲率算子的德里赫特问题的正径向解的存在性和不存在性。由于存在不同的权值（可能是奇异的或退化的），所考虑的问题显得相当微妙，它需要对解进行精确的定性分析，以及使用基于适当的 Pohozaev 类型标识的 Liouville 类型结果。此外，还给出了全局解具有振荡性的充分条件。

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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来源期刊

Mathematische Annalen 数学-数学

CiteScore

2.90

自引率

7.10%

发文量

181

审稿时长

4-8 weeks

期刊介绍： Begründet 1868 durch Alfred Clebsch und Carl Neumann. Fortgeführt durch Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguignon, Wolfgang Lück und Nigel Hitchin. The journal Mathematische Annalen was founded in 1868 by Alfred Clebsch and Carl Neumann. It was continued by Felix Klein, David Hilbert, Otto Blumenthal, Erich Hecke, Heinrich Behnke, Hans Grauert, Heinz Bauer, Herbert Amann, Jean-Pierre Bourguigon, Wolfgang Lück and Nigel Hitchin. Since 1868 the name Mathematische Annalen stands for a long tradition and high quality in the publication of mathematical research articles. Mathematische Annalen is designed not as a specialized journal but covers a wide spectrum of modern mathematics.