扩展域中准线性椭圆问题的多重正解

IF 1.6 2区数学 Q2 MATHEMATICS, APPLIED Applied Mathematics and Optimization Pub Date : 2024-06-29 DOI:10.1007/s00245-024-10155-0

Wulong Liu, Guowei Dai, Patrick Winkert, Shengda Zeng

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引用次数: 0

摘要

在本文中，我们利用变分法和 Lusternik-Schnirelmann 范畴理论，证明了在扩展域中不平衡增长的准线性椭圆问题存在多个正解。基于该范畴的性质，我们在扩展域和与问题相关的能量函数临界水平之间引入了合适的映射，从而可以通过域的形状来估计正解的数量。

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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Multiple Positive Solutions for Quasilinear Elliptic Problems in Expanding Domains

In this paper we prove the existence of multiple positive solutions for a quasilinear elliptic problem with unbalanced growth in expanding domains by using variational methods and the Lusternik–Schnirelmann category theory. Based on the properties of the category, we introduce suitable maps between the expanding domains and the critical levels of the energy functional related to the problem, which allow us to estimate the number of positive solutions by the shape of the domain.

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来源期刊

Applied Mathematics and Optimization 数学-应用数学

CiteScore

3.30

自引率

5.60%

发文量

103

审稿时长

>12 weeks

期刊介绍： The Applied Mathematics and Optimization Journal covers a broad range of mathematical methods in particular those that bridge with optimization and have some connection with applications. Core topics include calculus of variations, partial differential equations, stochastic control, optimization of deterministic or stochastic systems in discrete or continuous time, homogenization, control theory, mean field games, dynamic games and optimal transport. Algorithmic, data analytic, machine learning and numerical methods which support the modeling and analysis of optimization problems are encouraged. Of great interest are papers which show some novel idea in either the theory or model which include some connection with potential applications in science and engineering.