# Non-oscillation theorems

@article{Hille1948NonoscillationT, title={Non-oscillation theorems}, author={Einar Hille}, journal={Transactions of the American Mathematical Society}, year={1948}, volume={64}, pages={234-252} }

where F(x) is a real-valued function defined for x> 0 and belonging to L(E, 1/E) for each E>0. A solution of (1.1) is a real-valued function y(x), absolutely continuous together with its first derivative, which satisfies the equation for almost all x, in particular at all points of continuity of F(x). We shall say that the equation is non-oscillatory in (a, oo), a>O, if no solution can change its sign more than once in the interval. Since the zeros of linearly independent solutions separate… Expand

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