On Solutions of Systems of Differential Equations on Half-Line with Summable Coefficients

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