On the asymptotic behavior of solutions of third-order binomial differential equations (Q6552487)

The paper is devoted to the development of a method for constructing asymptotic formulas as \(x\rightarrow\infty\) for the fundamental solution system of two-term singular symmetric differential equations of odd order with coefficients in a broad class of functions that allow oscillation (with relaxed regularity conditions that do not satisfy the classical Titchmarsh-Levitan regularity conditions).\N\NThe main goal of this paper is to study the asymptotics of the fundamental solution system for cases of various behavior of the coefficients \(q(x)\) and \(h(x) = -1+1/\sqrt{p(x)}\) of a third-order third-order binomial equation \N\[\N\left(\frac{i}{2}\right)\left[(p(x)y')'' + (p(x)y'')'\right] + q(x)y = \lambda y.\N\]\NFor the case in which \(h(x) \notin L_1[1, \infty) \) new asymptotic formulas are obtained.\N\NThe results of the work are new and actual.