奇异拟线性问题正解的存在性、不存在性和多重性

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-09-21 DOI:10.14232/ejqtde.2022.1.13

R. L. Alves

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引用次数: 0

摘要

本文讨论了一个包含奇异项和参数超线性摄动的拟线性问题。我们对参数λ >0变化时正解的存在性、不存在性和多重性感兴趣。在第一个结果中，超线性扰动具有任意增长，并利用次超解法得到了问题解的存在性。对于第二个结果，超线性摄动具有亚临界增长，并利用山口定理证明了第二个解的存在性。

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Existence, nonexistence and multiplicity of positive solutions for singular quasilinear problems

In the present paper we deal with a quasilinear problem involving a singular term and a parametric superlinear perturbation. We are interested in the existence, nonexistence and multiplicity of positive solutions as the parameter λ > 0 varies. In our first result, the superlinear perturbation has an arbitrary growth and we obtain the existence of a solution for the problem by using the sub-supersolution method. For the second result, the superlinear perturbation has subcritical growth and we employ the Mountain Pass Theorem to show the existence of a second solution.

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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.