Abstract
In this paper we show that a result of S. W. Hawking and R. Penrose [Proc. Roy. Soc. London Ser. A, 314 (1970), pp. 529–548] on the existence of conjugate points for a real second order linear differential equation is a consequence of a much earlier result of M. Yelchin [5]. Yelchin’s original proof is clarified and corrected and his result is extended. As a result, we obtain extensions of the Hawking–Penrose theorem and Tipler’s [J. Differential Equations, 30 (1978), pp. 165–174] a complementary result to said theorem.
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