Singular solutions of semilinear elliptic equations with supercritical growth on Riemannian manifolds

被引：0
作者：
Shoichi Hasegawa
机构：
[1] Waseda University,Department of Mathematics, School of Fundamental Science and Engineering
来源：
Nonlinear Differential Equations and Applications NoDEA | 2024年 / 31卷
关键词：
Semilinear elliptic equation; Singular solution; Supercritical; Riemannian manifolds; Primary 58J05; Secondary 35J61; 35B40; 35A24;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
In this paper, we shall discuss singular solutions of semilinear elliptic equations with general supercritical growth on spherically symmetric Riemannian manifolds. More precisely, we shall prove the existence, uniqueness and asymptotic behavior of the singular radial solution, and also show that regular radial solutions converges to the singular solution. In particular, we shall provide these properties on spherically symmetric Riemannian manifolds including the hyperbolic space as well as the sphere.
引用
收藏
相关论文
共 77 条
[1]  
Bandle C(2002)The Brézis–Nirenberg problem on J. Differ. Equ. 178 264-279
[2]  
Benguria R(1998)Green’s function, harmonic transplantation, and best Sobolev constant in spaces of constant curvature Trans. Am. Math. Soc. 350 1103-1128
[3]  
Bandle C(2012)On the positive, “radial” solutions of a semilinear elliptic equation in Adv. Nonlinear Anal. 1 1-25
[4]  
Brillard A(2010)Imperfect bifurcations in nonlinear elliptic equations on spherical caps Commun. Pure Appl. Anal. 9 1189-1208
[5]  
Flucher M(1999)Best Sobolev constants and Emden equations for the critical exponent in Math. Ann. 313 83-93
[6]  
Bandle C(2011)The Fujita exponent for the Cauchy problem in the hyperbolic space J. Differ. Equ. 251 2143-2163
[7]  
Kabeya Y(2007)Non-radial clustered spike solutions for semilinear elliptic problems on J. Anal. Math. 102 181-208
[8]  
Bandle C(2008)Multiple clustered layer solutions for semilinear elliptic problems on Commun. Partial Differ. Equ. 33 613-635
[9]  
Kabeya Y(2023)Classification of radial solutions to J. Differ. Equ. 361 417-448
[10]  
Ninomiya H(2014) on Riemannian models J. Math. Pures Appl. (9) 102 1-35
12345678