Weighted boundary value problems for a second-order ordinary differential equation with singularity. I
The author considers the differential equation \(y''+p(x)y'-q(x)=f(x)\) on some interval (0,a], \(a>0\) with complex valued coefficients p, q and f, continuous in (0,a] and having, in general a singularity at \(x=0^+\), and studies the following boundary value problems for this equation: \(\lim_{x\to 0^+}\nu (x)y(x)=C_ 0\) \(y(a)=C_ 0\) and \(\lim \tau (x)y'(x)=C_ 0,\) \(y(a)=C_ a\), where \(C_ 0\), \(a_ 0\) are given complex numbers and where the weight functions \(\nu\) and \(\tau\) naturally depend on the singularities of p and q. The main result concerns the asymptotic properties of solutions to these problems in the case f(x)\(\equiv 0\).
scientific article; zbMATH DE number 4057948