1962
DOI: 10.2140/pjm.1962.12.945
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The behavior of solutions of ordinary, self-adjoint differential equations of arbitrary even order

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Cited by 22 publications
(30 citation statements)
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“…[Ui(x)}^ = (5) [t/uW]0"1L exactly m + 1 zeros on (a, b) and that these zeros lie between the first and last zeros of y}'_1,(x) on (a, b). Now, let x = x0 be the first zero of yt\~1)(x) on (a,c\ and assume, with no loss of generality, that y(x) > 0 on (a,c).…”
mentioning
confidence: 99%
“…[Ui(x)}^ = (5) [t/uW]0"1L exactly m + 1 zeros on (a, b) and that these zeros lie between the first and last zeros of y}'_1,(x) on (a, b). Now, let x = x0 be the first zero of yt\~1)(x) on (a,c\ and assume, with no loss of generality, that y(x) > 0 on (a,c).…”
mentioning
confidence: 99%
“…These results were subsequently extended to general even-order self-adjoint equations by Reid [13] and Hunt [9].…”
Section: Satisfying the Conditions Y(a) -Y'(a) -{Ry")(b) = (Ry")mentioning
confidence: 87%
“…Using this definition we obtain generalizations (in a direction different from that of [9] and [13]) of results of [11].…”
Section: Satisfying the Conditions Y(a) -Y'(a) -{Ry")(b) = (Ry")mentioning
confidence: 99%
“…The works of many authors relate in some way to the existence or nonexistence of solutions of (1) having (n, n)-zeros. Some specific references are Leighton and Nehari [5], Barrett [1], Reid [8], Hunt [4], Levin [6], Coppel [2], and Swanson [9]. An important aspect of the work of this paper is that the main theorem is proved without assuming equation (1) is selfadjoint while most of the work done to date requires selfadjointness.…”
Section: Jerry R Ridenhourmentioning
confidence: 99%