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<p>In this paper, we propose a method for constructing an asymptotic solution to a singularly perturbed Cauchy problem in the case of violation of the stability conditions for the spectrum of the limit operator. In particular, we consider a problem with a turning point where eigenvalues coincide at <InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(t=0\)</EquationSource> <EquationSource Format="MATHML"><math> <mrow> <mi>t</mi> <mo>=</mo> <mn>0</mn> </mrow> </math></EquationSource> </InlineEquation>.</p>

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SOLUTION OF THE SINGULARLY PERTURBED CAUCHY PROBLEM WITH A “WEAK” TURNING POINT OF THE LIMIT OPERATOR

  • 期刊论文

  • 发表日期：

    2026年2月1日

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  • A. G. Eliseev,
  • P. V. Kirichenko

摘要

In this paper, we propose a method for constructing an asymptotic solution to a singularly perturbed Cauchy problem in the case of violation of the stability conditions for the spectrum of the limit operator. In particular, we consider a problem with a turning point where eigenvalues coincide at \(t=0\) t = 0 .