Pavlíková, Elena A remark on the differential equation \(y''+q(x)y=r(x)\). (English) Zbl 0562.34022 Čas. Pěst. Mat. 109, 86-92 (1984). Consider the equation \(y''+q(x)y=r(x)\), \(q\in C_ 2(J)\), \(r\in C_ 0(J)\), J an open interval. In a previous paper [Acta Univ. Palacki. Olomuc., Fac. Rerum Nat., Math. 17, 27-33 (1978; Zbl 0429.34011)] M. Laitoch introduced the systems of knots of the 1st and 2nd kinds and gave a modification of Sturm’s theorem on separating zeros of solutions or zeros of the first derivatives of solutions of \(y''+q(x)y=0\). In this paper the author defines (inductively) accompanying equations of the form \(y''+{\mathbb{Q}}_ k(x)y=R_ k(x)\), where \(Q_ k\) and \(R_{\hat k}\) are appropriate functions of \(Q_{k-1}\) and \(R_{k-1}\) and their derivatives \((Q_ 0=q\), \(R_ 0=r)\), defines systems of knots of the \((2k+1)\) and \((2k+2)\) kinds and extends the results of Laitoch. Reviewer: F.R.Dias-Agudo Cited in 1 Document MSC: 34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations Keywords:Sturm’s theorem; separating zeros Citations:Zbl 0429.34011 × Cite Format Result Cite Review PDF Full Text: DOI