On the asymptotics of solutions of a singular \(n\)th-order differential equation with nonregular coefficients
Consider the linear differential equation \[y^{(2n)}(x)-(q(x)+h(x))y(x)=0_1\text{ for }x\in(0,\infty),\tag{*}\] where \(q\) is twice continuously differentiable and satisfies the Titchmarsh-Levitan-type regularity conditions and \(h\) is a rapidly oscillating perturbation. The authors present a scheme for constructing a fundamental system justifying the asymptotics as \(x\to\infty\).
asymptotic formula for solutions of differential equations
scientific article; zbMATH DE number 7035836