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International Journal of Differential Equations
Volume 2012, Article ID 296591, 34 pages
http://dx.doi.org/10.1155/2012/296591
Research Article

Radially Symmetric Solutions of

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

Received 31 May 2012; Accepted 10 August 2012

Academic Editor: Julio Rossi

Copyright © 2012 William C. Troy and Edward P. Krisner. 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. S. Chen, W. R. Derrick, and J. A. Cima, “Positive 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 · View at Google Scholar · View at Zentralblatt MATH
  2. A. Haraux and F. B. Weissler, “Nonuniqueness for a semilinear initial value problem,” Indiana University Mathematics Journal, vol. 31, no. 2, pp. 167–189, 1982. View at Publisher · View at Google Scholar
  3. D. D. Joseph and T. S. Lundgren, “Quasilinear Dirichlet problems driven by positive sources,” Archive for Rational Mechanics and Analysis, vol. 49, pp. 241–269, 1972/73. View at Google Scholar
  4. W. M. Ni and J. Serrin, “Existence and nonexistence theorems for ground states of quasilinear partial differential equations: the anomalous case,” Accademia Nazionale dei Lincei, vol. 77, pp. 231–257, 1986. View at Google Scholar
  5. P. Souplet and F. B. Weissler, “Regular 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 · View at Google Scholar · View at Zentralblatt MATH
  6. F. Merle and H. Zag, “Blowup estimates for nonlinear heat equations,” Methods and Applications of Analysis, vol. 8, pp. 551–556, 2001. View at Google Scholar
  7. V. A. Galaktionov and J. L. Vazquez, “Continuation of blowup solutions of nonlinear heat equations in several space dimensions,” Communications on Pure and Applied Mathematics, vol. 50, no. 1, pp. 1–67, 1997. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  8. S. Chen and W. R. Derrick, “Global existence and blow-up of solutions for a semilinear parabolic system,” The Rocky Mountain Journal of Mathematics, vol. 29, no. 2, pp. 449–457, 1999. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  9. L. A. Caffarelli, B. Gidas, and J. Spruck, “Asymptotic symmetry and local behavior of semilinear elliptic equations with critical Sobolev growth,” Communications on Pure and Applied Mathematics, vol. 42, no. 3, pp. 271–297, 1989. View at Google Scholar
  10. V. A. Galaktionov, “On blow-up “twistors” for the Navier Stokes equations in R3: a view from reaction-diffusion theory,” http://arxiv.org/abs/0901.4286.
  11. X. Wang, “On the Cauchy problem for reaction-diffusion equations,” Transactions of the American Mathematical Society, vol. 337, no. 2, pp. 549–590, 1993. View at Publisher · View at Google Scholar · View at Zentralblatt MATH
  12. E. A. Coddington and N. Levinson, Theory of Ordinary Differential Equations, McGraw-Hill, New York, NY, USA, 1955.
  13. F. Gazzola and H.-C. Grunau, “Radial entire solutions for supercritical biharmonic equations,” Mathematische Annalen, vol. 334, no. 4, pp. 905–936, 2006. View at Publisher · View at Google Scholar · View at Zentralblatt MATH