Naslov
Exact number of local extreme points of curvature function of solutions of secondorder linear differential equations

Autori
Chrayteh, Houssam ; Pašić, Mervan

Izvornik
Journal of applied mathematics and computing. International journal (1598-5865) 40 (2012); 5-32

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Curvature; Extreme points; Geometry of solutions; Linear differential equations

Sažetak
We study local properties of the curvature κy(x) of every nontrivial solution y = y(x) of the second-order linear differential equation (P ): (p(x)y')' + q(x)y = 0, x ∈ (a, b) = I , where p(x) and q(x) are smooth enough functions. It especially includes the Euler, Bessel and other important types of second-order linear differential equations. Some sufficient conditions on the coefficients p(x) and q(x) are given such that the curvature κy(x) of every nontrivial solution y of (P ) has exactly one extreme point between each two its consecutive simple zeros. The problem of three local extreme points of κy(x) is also considered but only as an open problem. It seems it is the first paper dealing with this kind of problems. Finally in Appendix, we pay attention to an application of the main results to a study of non-regular points (the cusps) of the ε-parallels of graph Γ (y) of y (the offset curves of Γ (y)).

Izvorni jezik
Engleski

Znanstvena područja
Matematika, Temeljne tehničke znanosti

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