非线性参数奇异狄利克雷问题的正解

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2018-07-20 DOI:10.1142/S1664360719500115

N. Papageorgiou, V. Rǎdulescu, Dušan D. Repovš

{"title":"非线性参数奇异狄利克雷问题的正解","authors":"N. Papageorgiou, V. Rǎdulescu, Dušan D. Repovš","doi":"10.1142/S1664360719500115","DOIUrl":null,"url":null,"abstract":"We consider a nonlinear parametric Dirichlet problem driven by the p-Laplace differential operator and a reaction which has the competing effects of a parametric singular term and of a Carathéodory perturbation which is ($$p-1$$p-1)-linear near $$+\\infty $$+∞. The problem is uniformly nonresonant with respect to the principal eigenvalue of $$(-\\Delta _p,W^{1,p}_0(\\Omega ))$$(-Δp,W01,p(Ω)). We look for positive solutions and prove a bifurcation-type theorem describing in an exact way the dependence of the set of positive solutions on the parameter $$\\lambda >0$$λ>0.","PeriodicalId":1,"journal":{"name":"Accounts of Chemical Research","volume":null,"pages":null},"PeriodicalIF":16.4000,"publicationDate":"2018-07-20","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"41","resultStr":"{\"title\":\"Positive solutions for nonlinear parametric singular Dirichlet problems\",\"authors\":\"N. Papageorgiou, V. Rǎdulescu, Dušan D. Repovš\",\"doi\":\"10.1142/S1664360719500115\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We consider a nonlinear parametric Dirichlet problem driven by the p-Laplace differential operator and a reaction which has the competing effects of a parametric singular term and of a Carathéodory perturbation which is ($$p-1$$p-1)-linear near $$+\\\\infty $$+∞. The problem is uniformly nonresonant with respect to the principal eigenvalue of $$(-\\\\Delta _p,W^{1,p}_0(\\\\Omega ))$$(-Δp,W01,p(Ω)). We look for positive solutions and prove a bifurcation-type theorem describing in an exact way the dependence of the set of positive solutions on the parameter $$\\\\lambda >0$$λ>0.\",\"PeriodicalId\":1,\"journal\":{\"name\":\"Accounts of Chemical Research\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":16.4000,\"publicationDate\":\"2018-07-20\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"41\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Accounts of Chemical Research\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://doi.org/10.1142/S1664360719500115\",\"RegionNum\":1,\"RegionCategory\":\"化学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"CHEMISTRY, MULTIDISCIPLINARY\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Accounts of Chemical Research","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1142/S1664360719500115","RegionNum":1,"RegionCategory":"化学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"CHEMISTRY, MULTIDISCIPLINARY","Score":null,"Total":0}

引用次数: 41

摘要

我们考虑了一个由p-拉普拉斯微分算子驱动的非线性参数Dirichlet问题和一个在$$+\infty $$ +∞附近具有参数奇异项和($$p-1$$ p-1)-线性的carathacimodory摄动的竞争效应的反应。该问题相对于$$(-\Delta _p,W^{1,p}_0(\Omega ))$$ (-Δp,W01,p(Ω))的主特征值是一致非共振的。我们寻找正解并证明了一个分岔型定理，该定理精确地描述了正解集对参数$$\lambda >0$$ λ>0的依赖关系。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

查看原文本刊更多论文

Positive solutions for nonlinear parametric singular Dirichlet problems

We consider a nonlinear parametric Dirichlet problem driven by the p-Laplace differential operator and a reaction which has the competing effects of a parametric singular term and of a Carathéodory perturbation which is ($$p-1$$p-1)-linear near $$+\infty $$+∞. The problem is uniformly nonresonant with respect to the principal eigenvalue of $$(-\Delta _p,W^{1,p}_0(\Omega ))$$(-Δp,W01,p(Ω)). We look for positive solutions and prove a bifurcation-type theorem describing in an exact way the dependence of the set of positive solutions on the parameter $$\lambda >0$$λ>0.

求助全文

通过发布文献求助，成功后即可免费获取论文全文。去求助

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.