On certain boundary value problems for second-order linear ordinary differential equations with singularities. (English) Zbl 0559.34012

Kiguradze, I. T.; Lomtatidze, A. G.

J. Math. Anal. Appl. 101, 325-347 (1984).

Authors’ summary: ”For the differential equation \(u''=p_ 1(t)u+p_ 2(t)u'+p_ 0(t)\) with locally integrable coefficients \(p_ k: | a,b| \to R\) \((k=0,1,2)\) and for each of the following three types of boundary conditions \(u(a+)=\alpha\), \(\lim_{t\to b-}u'(t)/\sigma (p_ 2)(t)=\beta\), \(u(a+)=\alpha\), \(u(b-)=\beta\), \(u(a+)=\alpha\), \(u(b- )=u(t_ 0)+\beta\), where \(-\infty <a<t_ 0<b<+\infty\) and \(\sigma (p_ 2)(t)=\exp (\int^{t}_{(a+b)/2}p_ 2(\tau)d\tau).\) The conditions for the existence and uniqueness of a solution are established.”

Reviewer: N.L.Maria

MSC:

34B05	Linear boundary value problems for ordinary differential equations
34A30	Linear ordinary differential equations and systems

Keywords:

locally integrable coefficients

References:

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