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Licensed Unlicensed Requires Authentication Published by De Gruyter July 30, 2013

Existence of a solution to the Dirichlet problem associated to a second-order differential equation with singularities: The method of lower and upper functions

  • Robert Hakl EMAIL logo and Manuel Zamora

Abstract.

This paper is devoted to the study of the existence of a solution to the Dirichlet boundary value problem for the second-order differential equation

where the functions satisfy the local Carathéodory conditions and may have singularities both in the time (for and ) and the phase (for and ) variables. Sufficient conditions for the solvability of the above-mentioned problem are established.

Received: 2012-09-18
Accepted: 2013-05-10
Published Online: 2013-07-30
Published in Print: 2013-09-01

© 2013 by Walter de Gruyter Berlin Boston

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