Cabada Fernández, AlbertoSaavedra López, Lorena2026-01-272026-01-272017-06Alberto 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)https://hdl.handle.net/10347/45439The 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.engAttribution-NonCommercial-NoDerivatives 4.0 Internationalhttp://creativecommons.org/licenses/by-nc-nd/4.0/Green's functionSpectral CharaterizationBeam equation1202 Análisis y análisis funcionaljournal article10.57262/ade/1489802456open access