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Dynamics of solutions of the simplest nonlinear boundary-value problems

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Abstract

We investigate two classes of essentially nonlinear boundary-value problems by using methods of the theory of dynamical systems and two special metrics. We prove that, for boundary-value problems of both these classes, all solutions tend (in the first metric) to upper semicontinuous functions and, under sufficiently general conditions, the asymptotic behavior of almost every solution can be described (by using the second metric) by a certain stochastic process.

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Authors
  1. E. Yu. Romanenko
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  2. A. N. Sharkovskii
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Additional information

Institute of Mathematics, Ukrainian Academy of Sciences, Kiev. Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 6, pp. 810–826, June, 1999.

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Romanenko, E.Y., Sharkovskii, A.N. Dynamics of solutions of the simplest nonlinear boundary-value problems. Ukr Math J 51, 907–925 (1999). https://doi.org/10.1007/BF02591978

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  • DOI: https://doi.org/10.1007/BF02591978

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