Nodal solutions for the nonlinear Robin problem in Orlicz spaces

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-08-12 DOI:10.1016/j.nonrwa.2024.104186

Anouar Bahrouni , Hlel Missaoui , Vicenţiu D. Rădulescu

引用次数: 0

Abstract

In this paper we consider a non-linear Robin problem driven by the Orlicz $g$ -Laplacian operator. Using variational technique combined with a suitable truncation and Morse theory (critical groups), we prove two multiplicity theorems with sign information for all the solutions. In the first theorem, we establish the existence of at least two non-trivial solutions with fixed sign. In the second, we prove the existence of at least three non-trivial solutions with sign information (one positive, one negative, and the other change sign) and order. The result of the nodal solution is new for the non-linear $g$ -Laplacian problems with the Robin boundary condition.

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奥利奇空间非线性罗宾问题的节点解

在本文中，我们考虑了一个由 Orlicz g-Laplacian 算子驱动的非线性 Robin 问题。利用变分技术结合适当的截断和莫尔斯理论（临界群），我们证明了所有解的两个带有符号信息的多重性定理。在第一个定理中，我们确定了至少存在两个具有固定符号的非微观解。在第二个定理中，我们证明了至少存在三个具有符号信息（一个正，一个负，另一个改变符号）和阶次的非微分解。对于具有 Robin 边界条件的非线性 g-Laplacian 问题来说，节点解的结果是新的。

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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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

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