disconjugate

— The disconjugate nystagmus, head titubation, and torticollis of spasmus nutans have been reported as indisinguishable from those associated with glioma of the anterior visual pathway.

— The aim of this paper consists on the study of the following fourth-order operator: \begin{equation}\label{Ec::T4} T[M]\,u(t)\equiv u^{(4)}(t)+p_1(t)\,u"'(t)+p_2(t)\,u"(t)+M\,u(t)\,,\ t\in I \equiv [a,b]\,, \end{equation} coupled with the two point boundary conditions: \begin{equation}\label{Ec::cf} u(a)=u(b)=u"(a)=u"(b)=0\,. \end{equation} So, we define the following space: \begin{equation}\label{Ec::esp} X=\left\lbrace u\in C^4(I)\quad\mid\quad u(a)=u(b)=u"(a)=u"(b)=0 \right\rbrace \,. \end{equation} Here p#95;1#92;inC³(I) and p#95;2#92;inC²(I). By assuming that the second order linear differential equation \begin{equation}\label{Ec::2or} L_2\, u(t)\equiv u"(t)+p_1(t)\,u'(t)+p_2(t)\,u(t)=0\,,\quad t\in I, \end{equation} is disconjugate on I, we characterize the parameter's set where the Green's function related to operator T#91;M#93; in X is of constant sign on I#92;timesI.