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Necessary and sufficient conditions for the existence of an “isolated” solution of a nonlinear two-point boundary-value problem

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A nonlinear two-point boundary-value problem for a system of ordinary differential equations is studied by splitting the interval and introducing additional parameters. We construct a system of equations with respect to the parameters, which enable us to determine the initial approximation to the solution of the boundary-value problem. We establish necessary and sufficient conditions for the existence of an isolated solution of the analyzed problem.

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Authors and Affiliations

  1. Institute of Mathematics, Ministry of Education and Science of Kazakhstan Republic, Kazakhstan, 050010, Alma-Ata, 125 Pushkina Str.

    D. S. Dzhumabaev & S. M. Temesheva

Authors
  1. D. S. Dzhumabaev
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  2. S. M. Temesheva
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Correspondence to D. S. Dzhumabaev.

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Translated from Neliniini Kolyvannya, Vol. 15, No. 4, pp. 435–446, October–December, 2012.

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Dzhumabaev, D.S., Temesheva, S.M. Necessary and sufficient conditions for the existence of an “isolated” solution of a nonlinear two-point boundary-value problem . J Math Sci 194, 341–353 (2013). https://doi.org/10.1007/s10958-013-1533-0

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  • DOI: https://doi.org/10.1007/s10958-013-1533-0

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