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ArticleOriginal scientific text

Title

An initial value problem fora third order differential equation

Authors 1

Affiliations

  1. Institute of Mathematics, University of Wrocław, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland

Abstract

For an initial value problem u'''(x) = g(u(x)), u(0) = u'(0) = u''(0) = 0, x > 0, some theorems on existence and uniqueness of solutions are established.

Keywords

ENG
nonlinear Volterra integral equation, existence and uniqueness of solutions

Bibliography

  1. P. J. Bushell and W. Okrasiński, Uniqueness of solutions for a class of nonlinear Volterra integral equations with convolution kernel, Math. Proc. Cambridge Philos. Soc. 106 (1989), 547-552.
  2. G. Gripenberg, Unique solutions of some Volterra integral equations, Math. Scand. 48 (1981), 59-67.
  3. W. Mydlarczyk, The existence of nontrivial solutions of Volterra equations, ibid. 68 (1991), 83-88.
  4. W. Okrasiński, Nontrivial solutions to nonlinear Volterra integral equations, SIAM J. Math. Anal. 22 (1991), 1007-1015.
  5. W. Okrasiński, Nontrivial solutions for a class of nonlinear Volterra equations with convolution kernel, J. Integral Equations Appl. 3 (1991), 399-409.
Annales Polonici Mathematici
1994/59/3
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Pages:
215-223
Main language of publication
English
Received
1993-01-25
Accepted
1993-06-03
Published
1994
Exact and natural sciences