A priori estimates of solutions of an even-order ordinary differential equation with a spectral parameter and integral conditions.

We consider an even-order ordinary differential operator with a spectral parameter and integral conditions. Constructive sufficient conditions for the discreteness of the spectrum and an a priori estimate of solutions to a non-local problem with integral conditions are obtained. The use of methods of nonlocal elliptic problems with a parameter made it possible to obtain the specified a priori estimate of solutions in terms of equivalent norms. However, unlike boundary value problems for elliptic differential equations with a parameter and non-local elliptic problems, this estimate contains an additional multiplier $|\lambda|^{1/2}$.