Oscillation criteria for the Schrödinger PDE (Q2733865)

This paper deals with the Schrödinger partial differential equation NEWLINE\[NEWLINE\Delta u+ C(x)u= 0,\tag{1}NEWLINE\]NEWLINE where the function \(C(x)\) is assumed to be integrable on each compact subset of the set \(\Omega= \{x\in\mathbb{R}^n\mid \|x\|\geq 1\}\). The main goal is to present some new oscillation criteria, that is criteria which guarantees that if there exists a solution \(u(x)\) of the equation (1) on \(\Omega\), then the function \(u\) is oscillatory.