RT Journal Article
T1 Constant sign Green's function for simply supported beam equation
A1 Cabada Fernández, Alberto
A1 Saavedra López, Lorena
K1 Green's function
K1 Spectral Charaterization
K1 Beam equation
AB 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\text{ satisfies boundary conditions \eqref{Ec::cf}}\right\rbrace \,.		\end{equation}		Here $p_1\in C^3(I)$ and $p_2\in C^2(I)$.	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 $T[M]$ in $X$ is of constant sign on $I \times I$. Such characterization is equivalent to the strongly inverse positive (negative) character of operator $T[M]$ on $X$ and comes from the first eigenvalues of operator $T[0]$ on suitable spaces.
PB Khayyam Publishing, Inc.
YR 2017
FD 2017-06
LK https://hdl.handle.net/10347/45439
UL https://hdl.handle.net/10347/45439
LA eng
NO Alberto Cabada, Lorena Saavedra "Constant sign Green's function for simply supported beam equation," Advances in Differential Equations, Adv. Differential Equations 22(5/6), 403-432, (May/June 2017)
NO Partially supported by Ministerio de Educacion, Cultura y Deporte, Spain and FEDER, project MTM2013-43014-P.
DS Minerva
RD 24 abr 2026