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On the number of solutions of a third-order boundary value problem

Author: Eva Rovderová
Journal: Trans. Amer. Math. Soc. 347 (1995), 3079-3092
MSC: Primary 34B15
MathSciNet review: 1243172
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Abstract: This paper deals with the number of solutions of the third-order boundary value problem $ y''' = f(t,y,y',y'')$, $ y(0) = {A_0}$, $ y'(0) = {A_1}$, $ y''(T) = B$. This number of solutions is investigated in connection with the number of zeros of a solution for the corresponding variational problem.

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  • [1] S. Fučík and A. Kufner, Nonlinear differential equations, SNTL, Prague, 1978. (Czech)
  • [2] Michal Greguš and Milan Gera, Some results in the theory of a third-order linear differential equation, Ann. Polon. Math. 42 (1983), 93–102. MR 728072,
  • [3] M. Greguš, M. Švec, and V. Šeda, Ordinary differential equations, Alfa, Bratislava, 1985. (Slovak)
  • [4] M. Greguš, Linear differential equation of the third order, Veda, Bratislava, 1981. (Slovak)
  • [5] Philip Hartman, Ordinary differential equations, John Wiley & Sons, Inc., New York-London-Sydney, 1964. MR 0171038
  • [6] M. A. Krasnosel′skiĭ, \cyr Polozhitel′nye resheniya operatornykh uravneniĭ., Gosudarstv. Izdat. Fiz.-Mat. Lit., Moscow], 1962 (Russian). MR 0145331
  • [7] B. N. Petrov, V. Yu. Rutkovskii, and S. D. Zemlyakov, Adaptive coordinate-parameter control of flying apparatuses, control in cosmic space, vol. 1, Nauka, Moscow, 1972. (Russian)
  • [8] V. Rocard, Dynamique générale des vibrations, Masson, Paris, 1949. (French)
  • [9] E. Rovderová, The number of solutions of two point nonlinear boundary value problems, Dissertation Thesis, 1993.
  • [10] E. Sadyrbaev, About the number of solutions of the two point boundary value problem, Latvian Math. Ann. 32 (1988), 37-41. (Russian)
  • [11] N. I. Vasiliev and Ju. A. Klokov, The elements of theory of boundary value problems for ordinary differential equations, Zinatne, Riga, 1978. (Russian)

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Keywords: Third-order nonlinear differential equations, boundary conditions, variation equation, index of a solution
Article copyright: © Copyright 1995 American Mathematical Society

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