Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8900108 | Journal of Mathematical Analysis and Applications | 2018 | 16 Pages |
Abstract
In this paper, we consider the following Kirchhoff-type problem{(a+λâ«R3|âu|2dx+λbâ«R3|u|2dx)(âÎu+bu)=f(u),inR3,uâH1(R3),u>0,inR3, where λâ¥0 is a parameter, a, b are positive constants and f reaches the critical growth. Without the Ambrosetti-Rabinowitz condition, we prove the existence of positive solutions for the Kirchhoff-type problem with a general critical nonlinearity. We also study the asymptotics of solutions as λâ0. Numerical solutions for related problems will be discussed in the second part.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Huixing Zhang, Cong Gu, Chun-Ming Yang, Jean Yeh, Juan Jiang,