A boundary value problem for the Sturm–Liouville equation with piecewise entire potential on the curve and solution discontinuity conditions

For large values of the spectral parameter module, the asymptotics of solutions of the standard Sturm–Liouville equation with a piecewise-entire potential along an lying in the complex plane arbitrary shape curve with a finite number of points in which the solutions and (or) their derivatives undergo discontinuities independent of the spectral parameter is obtained. The eigenvalue problem is investigated for the case of decaying boundary conditions.