Positivity preserving properties have been conjectured for the bilaplace Dirichlet problem in many versions. In this note we show that in any dimension there exist bounded smooth domains Ω such that even the solution of ∆u = 1 in Ω with the homogeneous Dirichlet boundary conditions u = uν = 0 on ∂Ω is sign-changing. In two dimensions this corresponds to the Kirchhoff-Love model of a clamped pla...

We examine the question of how the ranking between di erent distributions with respect to a one-parameter family of weight functions depend on the parameter. We argue that in this context sign regularity of the family of weight functions is a natural condition to consider. Several classical economical examples are shown to satisfy this condition. We use sign regularity to obtain results on the ...

In this paper, a class of nonlinear fractional differential equations with periodic boundary condition is investigated. Although the nonlinearity equation and Green’s function are sign-changing, results existence nonexistence positive solutions obtained by using Schaefer’s fixed-point theorem. Finally, two examples given to illustrate main results.

We consider a class of eigenvalue problems involving coefficients changing sign on the domain of interest. We describe the main spectral properties of these problems according to the features of the coefficients. Then, under some assumptions on the mesh, we explain how one can use classical finite element methods to approximate the spectrum as well as the eigenfunctions while avoiding spurious ...