Some new results on a linear equation of the second order
Work on solving the second order linear oscillation defined by Eq. (1.1), with continuous and positive coefficient ?(x) ? ( x ) that satisfies Lipschitzs condition on semi-axis [0,+?) [ 0 , + ? ) and the divergence of ? 0 + ? ( ? ? G ? 2 ) d x , had started since the 1830s with Sturms theorems. This paper presents generalizations as well as a simplification of classical Sturms theorems on the location and the position of zero oscillations, which have not been included in Amrein etal. (2005)[5]. Besides, according to results from Dimitrovski and Mijatovi? (1997)[1], Dimitrovski etal. (2007)[2] and Dimitrovski etal. (2007)[4], we add some ideas and supplements (Theorems 2.42.8, 2.10 and 2.11) to the classical Sturms theory of oscillations.
amplitude equation series-iteration method euclidean sine and cosine sturms functions