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In this study, the boundary-value problem with eigenvalue parameter generated by the differential equation with discontinuous coefficients and boundary conditions which contains not only endpoints of the considered interval, but also point of discontinuity and abstract linear functionals is investigated. So, the problem is not pure boundary-value.The authors single out a class of linear functionals and find simple algebraic conditions on coefficients, which garantee the existence ofinfinit number eigenvalues. Also the asymptotic formulas for eigenvalues are found.