Singular non-autonomous (p,q)-equations with competing nonlinearities

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2024-09-23 DOI:10.1016/j.nonrwa.2024.104225

Nikolaos S. Papageorgiou , Dongdong Qin , Vicenţiu D. Rădulescu

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引用次数: 0

Abstract

We consider a parametric non-autonomous

(p, q)

-equation with a singular term and competing nonlinearities, a parametric concave term and a Carathéodory perturbation. We consider the cases where the perturbation is

(p - 1)

-linear and where it is

(p - 1)

-superlinear (but without the use of the Ambrosetti–Rabinowitz condition). We prove an existence and multiplicity result which is global in the parameter

λ > 0

(a bifurcation type result). Also, we show the existence of a smallest positive solution and show that it is strictly increasing as a function of the parameter. Finally, we examine the set of positive solutions as a function of the parameter (solution multifunction). First, we show that the solution set is compact in

C_{0}^{1} (\bar{Ω})

and then we show that the solution multifunction is Vietoris continuous and also Hausdorff continuous as a multifunction of the parameter.

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具有竞争非线性的奇异非自治 (p,q) -方程

我们考虑的是一个参数非自治 (p,q) -方程，它包含一个奇异项和相互竞争的非线性、一个参数凹项和一个卡拉瑟奥多里扰动。我们考虑了扰动为 (p-1)- 线性和 (p-1)- 超线性（但不使用 Ambrosetti-Rabinowitz 条件）的情况。我们证明了参数 λ>0 全局性的存在性和多重性结果（分岔类型结果）。此外，我们还证明了一个最小正解的存在，并证明它作为参数的函数是严格递增的。最后，我们研究了作为参数函数的正解集（解的多重函数）。首先，我们证明解集在 C01(Ω̄) 中是紧凑的，然后我们证明解的多重函数是 Vietoris 连续的，并且作为参数的多重函数也是 Hausdorff 连续的。

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

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.