Abstract
We show the existence and gradient estimates of periodic solutions
in the case of
We show the existence and gradient estimates of periodic solutions
in the case of
N. D. Alikakos and L. C. Evans, “Continuity of the gradient for weak solutions of a degenerate parabolic equation,” Journal de Mathématiques Pures et Appliquées. Neuvième Série, vol. 62, no. 3, pp. 253–268, 1983.
View at: Google Scholar | Zentralblatt MATH | MathSciNetM. J. Esteban, “On periodic solutions of superlinear parabolic problems,” Transactions of the American Mathematical Society, vol. 293, no. 1, pp. 171–189, 1986.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetD. W. Bange, “Periodic solutions of a quasilinear parabolic differential equation,” Journal of Differential Equations, vol. 17, no. 1, pp. 61–72, 1975.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetT. I. Seidman, “Periodic solutions of a non-linear parabolic equation,” Journal of Differential Equations, vol. 19, no. 2, pp. 242–257, 1975.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetJ. L. Boldrini and J. Crema, “On forced periodic solutions of superlinear quasi-parabolic problems,” Electronic Journal of Differential Equations, vol. 1998, no. 14, pp. 1–18, 1998.
View at: Google Scholar | Zentralblatt MATH | MathSciNetN. Mizoguchi, “Periodic solutions for degenerate diffusion equations,” Indiana University Mathematics Journal, vol. 44, no. 2, pp. 413–432, 1995.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetM. Nakao, “Periodic solutions of some nonlinear degenerate parabolic equations,” Journal of Mathematical Analysis and Applications, vol. 104, no. 2, pp. 554–567, 1984.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetM. Nakao and Y. Ohara, “Gradient estimates of periodic solutions for some quasilinear parabolic equations,” Journal of Mathematical Analysis and Applications, vol. 204, no. 3, pp. 868–883, 1996.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetY.-F. Wang, J.-X. Yin, and Z.-Q. Wu, “Periodic solutions of evolution -Laplacian equations with nonlinear sources,” Journal of Mathematical Analysis and Applications, vol. 219, no. 1, pp. 76–96, 1998.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetY.-F. Wang, J.-X. Yin, and Z.-Q. Wu, “Periodic solutions of porous medium equations with weakly nonlinear sources,” Northeastern Mathematical Journal, vol. 16, no. 4, pp. 475–483, 2000.
View at: Google Scholar | Zentralblatt MATH | MathSciNetY.-F. Wang, Z.-Q. Wu, and J.-X. Yin, “Periodic solutions of evolution -Laplacian equations with weakly nonlinear sources,” International Journal of Mathematics, Game Theory, and Algebra, vol. 10, no. 1, pp. 67–77, 2000.
View at: Google Scholar | Zentralblatt MATH | MathSciNetC.-S. Chen and R.-Y. Wang, “ estimates of solution for the evolution -Laplacian equation with initial value in ,” Nonlinear Analysis, vol. 48, no. 4, pp. 607–616, 2002.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetJ. Crema and J. L. Boldrini, “More on forced periodic solutions of quasi-parabolic equations,” Cadernos de Matemática, vol. 1, no. 1, pp. 71–88, 2000.
View at: Google ScholarE. DiBenedetto, Degenerate Parabolic Equations, Universitext, Springer, New York, NY, USA, 1993.
View at: Zentralblatt MATH | MathSciNet