The distribution of zeros of solutions for a class of third order differential equation

• Cesarano, Clemente ^[2] ; Arahet, Mohammed A. ^[1] ; Al-Shami, Tareq M.
  1. [1] Amran University

     Amran University

     Yemen

     
  2. [2] International Telematic University UNINETTUNO.
• Localización: Proyecciones: Journal of Mathematics, ISSN 0716-0917, ISSN-e 0717-6279, Vol. 40, Nº. 5, 2021, págs. 1301-1321
• Idioma: inglés
• DOI: 10.22199/issn.0717-6279-4002
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• Resumen

  • For third order linear differential equations of the form r(t)x'(t)''+ p(t)x'(t) + q(t)x(t) = 0;we will establish lower bounds for the distance between zeros of a solution and/or its derivatives. The main results will be proved by making use of Hardyís inequality, some generalizations of Opialís inequality and Boydís inequality.

• Referencias bibliográficas
  • R. P. Agarwal and P. R. Krinamoorthy, “On the uniqueness of solutions of nonlinear boundary value problems”, Journal of Mathematical Physics,...
  • R. P. Agarwal and P. Pang, Opial Inequalities with Applications in Differential and Difference Equations. Dordrecht: Kluwer Academic, 1995.
  • P. R. Beesak and K. M. Das, “Extensions of Opial’s inequality”, Pacific Journal of Mathematics, vol. 26, pp. 215-232, 1968.
  • D. Boyd, “Best constants in a class of integral inequalities”, Pacific Journal of Mathematics, vol. 30, pp. 367-383, 1969.
  • I. Brnetić and J. Pečarić, “Some new Opial-type inequalities”, Mathematical Inequalities & Applications, vol. 1, no. 3, pp. 385-390, 1998.
  • G. Casadei, “Sul teorema di unicità di De La Vallée Poussin per equazioni differenziali del terzo ordine”, Rendiconti del Seminario Matematico...
  • S. Clark and D. Hinton, “Some disconjugacy criteria for differential equations with oscillatory coefficients”, Mathematische Nachrichten,...
  • A. M. Fink, “On Opial’s inequality for fn”, Proceedings of the American Mathematical Society, vol. 155, pp. 177-181, 1992.
  • A. Kufner and L.-E. Persson, Weighted Inequalities of Hardy Type. River Edge, NJ: World Scientific, 2003.
  • A. Kufner, L. Maligranda, and L. Persson, The Hardy Inequalities: About Its History and Some Related Results. Pilsen: Vydavatelský servis,...
  • A. Lasota, “Sur la distance entre les zéros de l'équation différentielle linéaire du troisième ordre”, Annales Polonici Mathematici, vol....
  • A. M. Liapounoff, “Problème général de la stabilité du mouvement”, Annales de la Faculté des sciences de Toulouse: Mathématiques, vol. 9,...
  • R. M. Mathsen, “A Disconjugacy condition for y’’’ +a2y’’ +a1y’ +a0y = 0”, Proceedings of the American Mathematical Society,...
  • O. Niccoletti, “Sulle consizioni iniziali che determinano gli integrale delle equazioni differenziali ordinarie”, Atti della Accademia delle...
  • E. Picard, “Mémoire sur la théorie des équations aux dérivées partielleset la méthode des approximations successives”, Journal de Mathématiques...
  • E. Picard, “Sur l'application des méthodes d'approximations successives à l'étude de certaines équations différentielles ordinaires”,...
  • U. Richard, “Metodi diversi per ottenere diseguaglianze alla De La Vallée Poussin nelle equazioni differenziali ordinarie del secondo e terzo...
  • S. H. Saker, B., Sudha, M. A. Arahet, and E., Thandapani, “Distribution of zeros of second order superlinear and sublinear neutral delay differential...
  • S. H. Saker, “Applications of Opial and Wirtinger inequalities on zeros of third order differential equations”, Dynamic Systems and Applications,...
  • S. H. Saker, “Lyapunov type inequalities for a second order differential equations with a damping term”, Annales Polonici Mathematici, vol....
  • S. H. Saker and M. A. Arahet, “Distributions of Zeros of Solutions for Third-Order Differential Equations with Variable Coefficients”, Mathematical...
  • C. de la Vallée Poussin, “Sur l'équation différentielle linéaire du second ordre. Détermination d'une intégrale par deux valeurs assignées....
  • X. Yang, “On Liapunov-type inequality for a certain higher-order differential equations”, Applied Mathematics and Computation, vol. 134, no....