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Boundary value conditions for linear differential equations with power degenerations

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On the interval [ 0 , 1 ] $[0,1]$ we consider the n th order linear differential equation, the coefficient of the highest derivative of which is equivalent to the… Click to show full abstract

On the interval [ 0 , 1 ] $[0,1]$ we consider the n th order linear differential equation, the coefficient of the highest derivative of which is equivalent to the power function t μ $t^{\mu }$ when t → 0 $t\rightarrow 0$ . The main aim of the paper is to pose “generalized” Cauchy conditions for the given equation at the point of singularity t = 0 $t=0$ , which would be correct for any μ > 0 $\mu >0$ .

Keywords: power; linear differential; boundary value; value conditions; conditions linear

Journal Title: Boundary Value Problems
Year Published: 2020

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