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Perturbation theory for the Sturm-Liouville problem with variable coefficients. (English. Russian original) Zbl 0818.34015
Comput. Math. Math. Phys. 34, No. 3, 417-419 (1994); translation from Zh. Vychisl. Mat. Mat. Fiz. 34, No. 3, 491-494 (1994).
Using the example of the problem $$(d^ 2/dx^ 2+ \lambda r(x)) \psi(x)= 0$$, $$\alpha_ a \psi(a)- \psi'(a)= 0$$, $$\alpha_ b \psi(b)+ \psi'(b)= 0$$, $$r> 0$$, with coefficient $$r(x)$$ of fairly arbitrary form, we consider the possibility of an analytic solution of the Sturm-Liouville problem by the methods of ordinary perturbation theory.
##### MSC:
 34B24 Sturm-Liouville theory 34E10 Perturbations, asymptotics of solutions to ordinary differential equations