Journal of Mathematical Sciences

, Volume 230, Issue 5, pp 742–745 | Cite as

On the Solvability of a Boundary-Value Problem for a Second-Order Singular Quasilinear Equation

  • V. P. Plaksina
  • I. M. Plaksina
  • E. V. Plekhova


We obtain solvability conditions for a two-point boundary-value problem for a second-order quasilinear equation. The equation is singular with respect to the independent variable. The result is based on the properties of the Green operator of the corresponding linear problem. In particular, we prove its boundedness and obtain an upper estimate of its norm. Conditions of existence of a solution of the original problem are obtained from the solvability condition of an auxiliary operator equation.

Keywords and phrases

singular ordinary differential equation boundary-value problem Green operator quasilinear equation 

AMS Subject Classification

34B05 34B16 


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Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  • V. P. Plaksina
    • 1
  • I. M. Plaksina
    • 1
  • E. V. Plekhova
    • 1
  1. 1.Perm National Research Polytechnic UniversityPermRussia

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