Determining bounds for the first conjugate point
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The purpose of this paper is to provide relatively simple methods for the determination of useful upper and lower bounds for the first zero greater than a of solutions of systems y″+p(x)y=0, y(a)=0, where p(x) is positive and continuous on an interval [a, b] and is either convex or concave there. On occasion, p(x) is required to be of class C′ or of class C″.
KeywordsLower Bound Conjugate Point
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- Walter Leigthon,On the zeros of solutions of a second-order linear differential equation, Jour. de Math. pures et appl., 44 (1965), pp. 297–310.Google Scholar
- -- --,Bounds for conjugate points, to appear in Journal für die reine und angewandte Mathematik.Google Scholar
- A. Samanich Skidmore andWalter Leighton,On the oscillation of solutions of a second-order linear differential equation, Rend. Mat. di Palermo, Serie II, 14 (1965), pp. 1–8.Google Scholar
- G. N. Watson,A treatise on the theory of Bessel functions, Cambridge Univ. Press, 2nd edit., 1966.Google Scholar