Journal of Mathematical Sciences

, Volume 149, Issue 5, pp 1504–1516

On the solvability of a singular boundary-value problem for the equation f(t, x, x′, x″) = 0

  • M. K. Grammatikopoulos
  • P. S. Kelevedjiev
  • N. I. Popivanov
Article

Abstract

In this work, we consider boundary-value problems of the form
$$f(t, x, x', x'') = 0, 0 < t < 1, x(0) = 0, x'(1) = b, b > 0$$
, where the scalar function f(t, x, p, q) may be singular at x = 0. As far as we know, the solvability of the singular boundary-value problems of this form has not been treated yet. Here we try to fill in this gap. Examples illustrating our main result are included.

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Copyright information

© Springer Science+Business Media, Inc. 2008

Authors and Affiliations

  • M. K. Grammatikopoulos
    • 1
  • P. S. Kelevedjiev
    • 2
  • N. I. Popivanov
    • 3
  1. 1.Department of MathematicsUniversity of IoanninaIoanninaGreece
  2. 2.Department of MathematicsTechnical University of SlivenSlivenBulgaria
  3. 3.Department of Mathematics“St. Kl. Ohridski” University of SofiaSofiaBulgaria

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