2017/03/27 by Alberto Cabada, Cabada, Alberto, Lorena Saavedra +1
Mathematics · #Classical Analysis and ODEs (math.CA) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.1703.09107
openalex publication_date 2017/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The aim of this paper is to study the following fourth-order operator: T[p,c] u(t)≡ u(4)(t)-p u"(t)+c(t) u(t) , t∈ I≡ [a,b] , coupled with the non-homogeneous simply supported beam boundary conditions: u(a)=u(b)=0 , u"(a)=d1≤0 , u"(b)=d2≤ 0 . First, we prove a result which makes an equivalence between the strongly inverse positive (negative) character of this operator with the previously introduced boundary conditions and with the homogeneous boundary conditions, given by: T[p,c] u(t)=h(t)(≥0) , u(a)=u(b)=u"(a)=u"(b)=0 , Once that we have done that, we prove several results where the strongly inverse positive (negative) character of T[p,c] it is ensured. Finally, there are shown a couple of result which say that under the hypothesis that h>0, we can affirm that the problem for the homogeneous boundary conditions has a unique constant sign solution.