Limit circle/limit point criteria for second-order sublinear differential equations with damping term
Consider the scalar equation \[ (a(t)y')'+ b(t)y'+ r(t) y^\gamma= 0,\tag{\(*\)} \] where \(a,r: \mathbb R_+\to \mathbb R\) are sufficiently smooth, \(b: \mathbb R_+\to\mathbb R_+\) is continuous, \(\gamma= 2k-1\) with \(k= (M+ N- 1)/(2N- 1)\), where \(M\) and \(N\) are positive integers. The authors present necessary and sufficient conditions for \((*)\) to be of limit-circle type or limit-point type.
scientific article; zbMATH DE number 5997825