Ukrainian Mathematical Journal

, Volume 49, Issue 2, pp 204–215 | Cite as

Problem with nonlocal conditions for weakly nonlinear hyperbolic equations

  • T. P. Goi
  • B. I. Ptashnik


For weakly nonlinear hyperbolic equations of order n, n≥3, with constant coefficients in the linear part of the operator, we study a problem with nonlocal two-point conditions in time and periodic conditions in the space variable. Generally speaking, the solvability of this problem is connected with the problem of small denominators whose estimation from below is based on the application of the metric approach. For almost all (with respect to the Lebesgue measure) coefficients of the equation and almost all parameters of the domain, we establish conditions for the existence of a unique classical solution of the problem.


Periodic Solution Lebesgue Measure Nonlinear Integral Equation Nonlocal Condition Nonlocal Problem 
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© Plenum Publishing Corporation 1998

Authors and Affiliations

  • T. P. Goi
  • B. I. Ptashnik

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