Singular solutions for semilinear elliptic equations with general supercritical growth

被引：7

作者：

Miyamoto, Yasuhito ^{[1
]}

Naito, Yuki ^{[2
]}

机构：

[1] Univ Tokyo, Grad Sch Math Sci, Meguro Ku, 3-8-1 Komaba, Tokyo 1538914, Japan

[2] Hiroshima Univ, Dept Math, Higashihiroshima 7398526, Japan

来源：

ANNALI DI MATEMATICA PURA ED APPLICATA | 2023年 / 202卷 / 01期

关键词：

Singular solution; Supercritical; Asymptotic expansion; Bifurcation diagram; Super-exponential; BIFURCATION DIAGRAMS; POSITIVE SOLUTIONS; CLASSIFICATION;

D O I：

10.1007/s10231-022-01244-4

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

A positive radial singular solution for Delta u + f (u) = 0 with a general supercritical growth is constructed. An exact asymptotic expansion as well as its uniqueness in the space of radial functions are also established. These results can be applied to the bifurcation problem Delta u + lambda f (u) = 0 on a ball. Our method can treat a wide class of nonlinearities in a unified way, e.g., u(p) log u, exp(u(p)) and exp(center dot center dot center dot exp(u)center dot center dot center dot) as well as u(p) and e(u). Main technical tools are intrinsic transformations for semilinear elliptic equations and ODE techniques.

引用

页码：341 / 366

页数：26

共 26 条

[1]

[Anonymous], 1997, Rev. Mat. Univ. Complut. Madrid

[2] SEMILINEAR ELLIPTIC-EQUATIONS AND SUPERCRITICAL GROWTH [J].