Abstract. Let N be an integral operator of the formacting in Lp(R c ) with a measurable kernel n satisfying the estimatewhere β ∈ L 1 . It is proved that if the function t → n(t, ·) is continuous in the norm of L 1 and the operator 1 + N has an inverse, then (1 + N ) −1 = 1 + M , where M is an integral operator possessing the same properties.

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We consider a system of differential equations and obtain its solutions with exponential asymptotics and analyticity with respect to the spectral parameter. Solutions of such type have importance in studying spectral properties of differential operators. Here, we consider the system of first-order differential equations on a half-line with summable coefficients, containing a nonlinear dependence on the spectral parameter. We obtain fundamental systems of solutions with analyticity in certain sectors, in which it is possible to apply the method of successive approximations. We also construct non-fundamental systems of solutions with analyticity in a large sector, including two previously considered neighboring sectors. The obtained results admit applications in studying inverse spectral problems for the higher-order differential operators with distribution coefficients.

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