Table of Contents Author Guidelines Submit a Manuscript
International Journal of Mathematics and Mathematical Sciences
Volume 2011, Article ID 608576, 22 pages
http://dx.doi.org/10.1155/2011/608576
Research Article

Radially Symmetric Solutions of a Nonlinear Elliptic Equation

1Department of Mathematics, University of Pittsburgh at Greensburg, Greensburg, PA 15601, USA
2Department of Mathematics, University of Pittsburgh, Pittsburgh, PA 15260, USA

Received 30 December 2010; Accepted 18 April 2011

Academic Editor: Frank Werner

Copyright © 2011 Edward P. Krisner and William C. Troy. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Linked References

  1. H. Brezis, L. A. Peletier, and D. Terman, β€œA very singular solution of the heat equation with absorption,” Archive for Rational Mechanics and Analysis, vol. 95, no. 3, pp. 185–209, 1986. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  2. S. Kamin and L. A. Peletier, β€œSingular solutions of the heat equation with absorption,” Proceedings of the American Mathematical Society, vol. 95, no. 2, pp. 205–210, 1985. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  3. S. Kamin, L. A. Peletier, and J. L. Vázquez, β€œClassification of singular solutions of a nonlinear heat equation,” Duke Mathematical Journal, vol. 58, no. 3, pp. 601–615, 1989. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  4. A. Haraux and F. B. Weissler, β€œNon-uniqueness for a semilinear initial value problem,” Indiana University Mathematics Journal, vol. 31, no. 2, pp. 167–189, 1982. View at Publisher Β· View at Google Scholar
  5. P. Souplet and F. B. Weissler, β€œRegular self-similar solutions of the nonlinear heat equation with initial data above the singular steady state,” Annales de l'Institut Henri Poincaré, vol. 20, no. 2, pp. 213–235, 2003. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH Β· View at MathSciNet
  6. S. Chen and W. R. Derrick, β€œGlobal existence and blowup of solutions for of semilinear parabolic equation,” The Rocky Mountain Journal of Mathematics, vol. 29, no. 2, pp. 449–457, 1999. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  7. S. Chen, W. R. Derrick, and J. A. Cima, β€œPositive and oscillatory radial solutions of semilinear elliptic equations,” Journal of Applied Mathematics and Stochastic Analysis, vol. 10, no. 1, pp. 95–108, 1997. View at Publisher Β· View at Google Scholar Β· View at Zentralblatt MATH
  8. L. A. Peletier and W. C. Troy, Spatial Patterns: Higher Order Models in Physics and Mechanics, Birkhäuser, Boston, Mass, USA, 2001.