Remote Access Transactions of the American Mathematical Society
Green Open Access

Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)

 
 

 

The structure of solutions of a semilinear elliptic equation


Authors: Kuo-Shung Cheng and Tai Chia Lin
Journal: Trans. Amer. Math. Soc. 332 (1992), 535-554
MSC: Primary 35B05; Secondary 35B40, 35J60
DOI: https://doi.org/10.1090/S0002-9947-1992-1055568-1
MathSciNet review: 1055568
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: We give a complete classification of solutions of the elliptic equation $ \Delta u + K(x){e^{2u}} = 0$ in $ \mathbb{R}^n, n \geq 3$, for some interesting cases of $ K$.


References [Enhancements On Off] (What's this?)

  • [CL] K.-S. Cheng and J.-T. Lin, On the elliptic equations $ \Delta u = K{u^\sigma }$ and $ \Delta u = K{e^{2u}}$, Trans. Amer. Math. Soc. 304 (1987), 639-668. MR 911088 (88j:35054)
  • [CN1] K.-S. Cheng and W.-M. Ni, On the structure of the conformal Gaussian curvature equation on $ {\mathbb{R}^2}$, Duke Math. J. 62 (1991), 721-737. MR 1104815 (92f:35061)
  • [CN2] -, On the structure of the conformal scalar curvature equation on $ {\mathbb{R}^n}$, Indiana Univ. Math. J. (to appear).
  • [GT] D. Gilbarg and N. S. Trudinger, Elliptic partial differential equations of second order, 2nd ed., Springer-Verlag, 1983. MR 737190 (86c:35035)
  • [HK] W. K. Hayman and P. B. Kennedy, Subharmonic functions, vol. 1, London Math. Soc. Monographs, no. 9, Academic Press, London, 1976.
  • [K] J. Kazdan, Prescribing the curvature of a Riemannian manifold, CBMS Regional Conf. Ser. in Math., no. 57, Amer. Math. Soc., Providence, R.I., 1985. MR 787227 (86h:53001)
  • [KO] T. Kusano and S. Oharu, Bounded entire solutions of second order semilinear elliptic equation with application to a parabolic initial value problem, Indiana Univ. Math. J. 34 (1985), 85-89. MR 773394 (86i:35048)
  • [LC] J.-T. Lin and K.-S. Cheng, Examples of solution for semilinear elliptic equations, Chinese J. Math. 15 (1987), 43-59. MR 907154 (88k:35068)
  • [N1] W.-M. Ni, On the elliptic equation $ \Delta u + K{e^{2u}} = 0$ and conformal metrics with prescribed Gaussian curvatures, Invent. Math. 66 (1982), 343-352. MR 656628 (84g:58107)
  • [N2] -, On the elliptic equation $ \Delta u + K{u^{(n + 2)/(n - 2)}} = 0$, its generalizations and applications in geometry, Indiana Univ. Math. J. 31 (1982), 493-529. MR 662915 (84e:35049)
  • [O] O. A. Oleinik, On the equation $ \Delta u + K(x){e^u} = 0$, Russian Math. Surveys 33 (1978), 243-244. MR 0492838 (58:11900)

Similar Articles

Retrieve articles in Transactions of the American Mathematical Society with MSC: 35B05, 35B40, 35J60

Retrieve articles in all journals with MSC: 35B05, 35B40, 35J60


Additional Information

DOI: https://doi.org/10.1090/S0002-9947-1992-1055568-1
Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society