Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
7221884 | Nonlinear Analysis: Real World Applications | 2019 | 25 Pages |
Abstract
In this paper, we first show some necessary and sufficient conditions to the rapidly and regularly varying functions defined in Appendix A; in particular, we find that the rapidly varying function classes ââ and Gâ given in Definition A.4, Definition A.5, respectively, are not equivalent, i.e., âââ«Gâ. Thereafter, we establish the asymptotic behavior and uniqueness of entire large solutions to the semilinear elliptic equation Îu=b(x)f(u),xâRN(Nâ¥3), where bâC(RN) is positive in RN, fâC[0,â) is positive and non-decreasing on (0,â), and belongs to a more general class of functions. Additionally, we also study the asymptotic behavior and uniqueness of entire large solutions when fâGââââ.
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Authors
Haitao Wan, Xiaohong Li, Bo Li, Yongxiu Shi,