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
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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.
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共 77 条
[31]  
Véron L(2015)Symmetry breaking bifurcation from solutions concentrating on the equator of Ann. Mat. Pura Appl. (4) 194 931-952
[32]  
Bidaut-Véron M-F(2018)Structure of the positive solutions for supercritical elliptic equations in a ball Proc. Roy. Soc. Edinb. Sect. A 148 133-147
[33]  
Véron L(2023)Classification of bifurcation diagrams for elliptic equations with exponential growth in a ball Ann. Mat. Pura Appl. (4) 202 341-366
[34]  
Bonforte M(2011)Infinitely many non-radial singular solutions of J. Differ. Equ. 251 1972-1989
[35]  
Gazzola F(1994) in Topol. Methods Nonlinear Anal. 3 1-25
[36]  
Grillo G(undefined), undefined undefined undefined-undefined
[37]  
Vázquez JL(undefined)Singular solutions for semilinear elliptic equations with general supercritical growth undefined undefined undefined-undefined
[38]  
Brezis H(undefined)On well-posedness of semilinear parabolic and elliptic problems in the hyperbolic space undefined undefined undefined-undefined
[39]  
Peletier L(undefined)Classification of positive solutions of quasilinear elliptic equations undefined undefined undefined-undefined
[40]  
Budd C(undefined)undefined undefined undefined undefined-undefined
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