The Pohozaev-type inequalities and their applications for a kind of elliptic equation (system)

Boundary Value Problems

Tianqing An¹  Bingyu Kou²  Zeyan Wang² 

[1] College of Science, Hohai University;Department of Basic Courses, The Army Engineering University of PLA;

关键词: Pohozaev-type inequality;    p-Laplacian;    Non-star-shaped domain;    Variational methods;    Nonexistence and existence;    Double critical exponent;   

DOI  :  10.1186/s13661-020-01475-5

来源: DOAJ

【 摘 要 】

Abstract In this paper, we first derive a new kind of Pohozaev-type inequalities for p-Laplacian equations in a more general class of non-star-shaped domains, and then we take two examples and their graphs to explain the shape of the new kind of the non-star-shaped domain. At last, we extend the results of Pohozaev-type inequalities to elliptic systems, which are used to derive the nonexistence of positive solutions of this type of systems in the non-star-shaped domains. On this basis, we also discuss the existence of positive solutions of a kind of elliptic systems with double critical growth.

【 授权许可】

Unknown