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Uniqueness and parameter dependence of positive doubly periodic solutions of nonlinear telegraph equations

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
The authors study a type of second order nonlinear telegraph equation. The existence and uniqueness of positive doubly periodic solutions are discussed. The parametric dependence of the solutions is also investigated. Two examples are given as applications of the results.
Rocznik
Strony
363--373
Opis fizyczny
Bibliogr. 16 poz., rys., tab/
Twórcy
autor
  • Department of Mathematics University of Tennessee at Chattanooga Chattanooga, TN 37403, USA
autor
  • Department of Mathematics University of Tennessee at Chattanooga Chattanooga, TN 37403, USA
autor
  • Department of Mathematics University of Tennessee at Chattanooga Chattanooga, TN 37403, USA
Bibliografia
  • [1] D. Anderson, J. Tannehill, R. Pletcher, Computational Fluid Mechanics and Heat Transfer, McGraw-Hill, New York, 1984.
  • [2] C. Bereanu, An Ambrosetti-Prodi-type result for periodic solutions of the telegraph equation, Proc. Roy. Soc. Edinburgh Sect. A 138 (2008), 719–724.
  • [3] C. Bereanu, Periodic solutions of the nonlinear telegraph equations with bounded nonlinearities, J. Math. Anal. Appl. 343 (2008), 758–762.
  • [4] A. Dogan, J.R. Graef, L. Kong, Higher order singular multi-point boundary value problems on time scales, Proc. Edinburgh Math. Soc. 54 (2011), 345–361.
  • [5] M.S. El-Azab, M. El-Gamel, A numerical algorithm for the solution of telegraph equations, Appl. Math. Comput. 190 (2007), 757–764.
  • [6] M. Ghergu, V. Radulescu, Nonlinear PDEs. Mathematical Models in Biology, Chemistry and Population Genetics, Springer Monographs in Mathematics, Springer, Heidelberg, 2012.
  • [7] B.H. Gilding, R. Kersner, Wavefront solutions of a nonlinear telegraph equation, J. Differential Equations 254 (2013), 599–636.
  • [8] J.R. Graef, L. Kong, M. Wang, B. Yang, Uniqueness and parameter dependence of positive solutions of a discrete fourth order problem, J. Difference Equ. Appl. 19 (2013), 1133–1146.
  • [9] Y. Li, Maximum principles and the method of upper and lower solutions for time-periodic problems of the telegraph equations, J. Math. Anal. Appl. 327 (2007), 997–1009.
  • [10] Y. Li, Positive doubly periodic solutions of nonlinear telegraph equations, Nonlinear Anal. 55 (2003), 245–254.
  • [11] J. Mawhin, Maximum principle for bounded solutions of the telegraph equation: the case of high dimensions, [in:] Elliptic and parabolic problems, Progr. Nonlinear Differential Equations Appl., 63, Birkhäuser, Basel, 2005, 343–351.
  • [12] R. Ortega, A.M. Robles-Pérez, A maximum principle for periodic solutions of the telegraph equation, J. Math. Anal. Appl. 221 (1998), 625–651.
  • [13] F. Wang, Y. An, Multiple positive doubly periodic solutions for a singular semipositone telegraph equation with a parameter, Bound. Value Probl. 2013, 2013:7, 8 pp.
  • [14] F. Wang, Y. An, An Ambrosetti-Prodi-type result for doubly periodic solutions of the telegraph system, J. Math. Anal. Appl. 385 (2012), 582–588.
  • [15] F. Wang, Y. An, Doubly periodic solutions to a coupled telegraph system, Nonlinear Anal. 75 (2012), 1887–1894.
  • [16] C. Zhai, M. Hao, Fixed point theorems for mixed monotone operators with perturbation and applications to fractional differential equation boundary value problems, Nonlinear Anal. 75 (2012), 2542–2551.
Typ dokumentu
Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-fcbe5a56-dda6-407c-bed6-95187f8abe48
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