American Institute of Mathematical Sciences

Advanced
December  2005, 4(4): 871-888. doi: 10.3934/cpaa.2005.4.871

Structure of positive radial solutions including singular solutions to Matukuma's equation

Hiroshi Morishita 1, , Eiji Yanagida 2, and  Shoji Yotsutani 3,

1. 

Department of Economics and Information Science, Hyogo University, Kakogawa, 675-0101, Japan
2. 

Mathematical Institute Tohoku University, 6-3Aoba, Aramaki, Aoba-ku, Sendai-shi, 980-8578
3. 

Department of Applied Mathematics and Informatics, Ryukoku University, Seta, Otsu, 520-2194

Received  June 2005 Published  September 2005

We consider positive solutions of Matukuma's equation, which is described by a nonlinear elliptic equation with a weight. Any radially symmetric solution of this equation is said to be regular or singular according to its behavior near the origin and infinity. We investigate the structure of positive radial regular and singular solutions.
Keywords: Semilinear elliptic equation, radial solutions.
Mathematics Subject Classification: 35J25, 34B16.
Citation: Hiroshi Morishita, Eiji Yanagida, Shoji Yotsutani. Structure of positive radial solutions including singular solutions to Matukuma's equation. Communications on Pure & Applied Analysis, 2005, 4 (4) : 871-888. doi: 10.3934/cpaa.2005.4.871
[1]

Joseph A. Iaia. Localized radial solutions to a semilinear elliptic equation in $\mathbb{R}^n$. Conference Publications, 1998, 1998 (Special) : 314-326. doi: 10.3934/proc.1998.1998.314
[2]

Ruofei Yao, Yi Li, Hongbin Chen. Uniqueness of positive radial solutions of a semilinear elliptic equation in an annulus. Discrete & Continuous Dynamical Systems - A, 2019, 39 (3) : 1585-1594. doi: 10.3934/dcds.2018122
[3]

Zhuoran Du. Some properties of positive radial solutions for some semilinear elliptic equations. Communications on Pure & Applied Analysis, 2010, 9 (4) : 943-953. doi: 10.3934/cpaa.2010.9.943
[4]

Tomás Sanz-Perela. Regularity of radial stable solutions to semilinear elliptic equations for the fractional Laplacian. Communications on Pure & Applied Analysis, 2018, 17 (6) : 2547-2575. doi: 10.3934/cpaa.2018121
[5]

Sara Barile, Addolorata Salvatore. Radial solutions of semilinear elliptic equations with broken symmetry on unbounded domains. Conference Publications, 2013, 2013 (special) : 41-49. doi: 10.3934/proc.2013.2013.41
[6]

Soohyun Bae, Yūki Naito. Separation structure of radial solutions for semilinear elliptic equations with exponential nonlinearity. Discrete & Continuous Dynamical Systems - A, 2018, 38 (9) : 4537-4554. doi: 10.3934/dcds.2018198
[7]

Shoichi Hasegawa. Stability and separation property of radial solutions to semilinear elliptic equations. Discrete & Continuous Dynamical Systems - A, 2019, 39 (7) : 4127-4136. doi: 10.3934/dcds.2019166
[8]

Henri Berestycki, Juncheng Wei. On least energy solutions to a semilinear elliptic equation in a strip. Discrete & Continuous Dynamical Systems - A, 2010, 28 (3) : 1083-1099. doi: 10.3934/dcds.2010.28.1083
[9]

Yinbin Deng, Shuangjie Peng, Li Wang. Existence of multiple solutions for a nonhomogeneous semilinear elliptic equation involving critical exponent. Discrete & Continuous Dynamical Systems - A, 2012, 32 (3) : 795-826. doi: 10.3934/dcds.2012.32.795
[10]

Paolo Caldiroli. Radial and non radial ground states for a class of dilation invariant fourth order semilinear elliptic equations on $R^n$. Communications on Pure & Applied Analysis, 2014, 13 (2) : 811-821. doi: 10.3934/cpaa.2014.13.811
[11]

Futoshi Takahashi. An eigenvalue problem related to blowing-up solutions for a semilinear elliptic equation with the critical Sobolev exponent. Discrete & Continuous Dynamical Systems - S, 2011, 4 (4) : 907-922. doi: 10.3934/dcdss.2011.4.907
[12]

Tsung-Fang Wu. Multiplicity of positive solutions for a semilinear elliptic equation in $R_+^N$ with nonlinear boundary condition. Communications on Pure & Applied Analysis, 2010, 9 (6) : 1675-1696. doi: 10.3934/cpaa.2010.9.1675
[13]

Jiabao Su, Rushun Tian. Weighted Sobolev embeddings and radial solutions of inhomogeneous quasilinear elliptic equations. Communications on Pure & Applied Analysis, 2010, 9 (4) : 885-904. doi: 10.3934/cpaa.2010.9.885
[14]

Andrés Contreras, Manuel del Pino. Nodal bubble-tower solutions to radial elliptic problems near criticality. Discrete & Continuous Dynamical Systems - A, 2006, 16 (3) : 525-539. doi: 10.3934/dcds.2006.16.525
[15]

Dagny Butler, Eunkyung Ko, Eun Kyoung Lee, R. Shivaji. Positive radial solutions for elliptic equations on exterior domains with nonlinear boundary conditions. Communications on Pure & Applied Analysis, 2014, 13 (6) : 2713-2731. doi: 10.3934/cpaa.2014.13.2713
[16]

Zongming Guo, Xuefei Bai. On the global branch of positive radial solutions of an elliptic problem with singular nonlinearity. Communications on Pure & Applied Analysis, 2008, 7 (5) : 1091-1107. doi: 10.3934/cpaa.2008.7.1091
[17]

Elisa Calzolari, Roberta Filippucci, Patrizia Pucci. Existence of radial solutions for the $p$-Laplacian elliptic equations with weights. Discrete & Continuous Dynamical Systems - A, 2006, 15 (2) : 447-479. doi: 10.3934/dcds.2006.15.447
[18]

M. Grossi. Existence of radial solutions for an elliptic problem involving exponential nonlinearities. Discrete & Continuous Dynamical Systems - A, 2008, 21 (1) : 221-232. doi: 10.3934/dcds.2008.21.221
[19]

Yinbin Deng, Shuangjie Peng, Li Wang. Infinitely many radial solutions to elliptic systems involving critical exponents. Discrete & Continuous Dynamical Systems - A, 2014, 34 (2) : 461-475. doi: 10.3934/dcds.2014.34.461
[20]

João Marcos do Ó, Sebastián Lorca, Justino Sánchez, Pedro Ubilla. Positive radial solutions for some quasilinear elliptic systems in exterior domains. Communications on Pure & Applied Analysis, 2006, 5 (3) : 571-581. doi: 10.3934/cpaa.2006.5.571

2018 Impact Factor: 0.925

Tools

Metrics

  • PDF downloads (12)
  • HTML views (0)
  • Cited by (3)

Other articles
by authors

[Back to Top]

Copyright © 2019 American Institute of Mathematical Sciences