### A boundary value problem of fractional order at resonance.

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The existence of classical solutions for some partial differential equations on tori is shown.

In this article the essential spectrum of closed, densely defined linear operators is characterized on a large class of spaces, which possess the Dunford-Pettis property or which isomorphic to one of the spaces ${L}_{p}\left(\mathrm{\Omega}\right)$$p>1$. A practical...

We study the existence of positive solutions to a class of singular nonlinear fourth-order boundary value problems in which the nonlinearity may lack homogeneity. By introducing suitable control functions and applying cone expansion and cone compression, we prove three existence theorems. Our main results improve the existence result in [Z. L. Wei, Appl. Math. Comput. 153 (2004), 865-884] where the nonlinearity has a certain homogeneity.

The aim of this paper is to develop a crowd motion model designed to handle highly packed situations. The model we propose rests on two principles: we first define a spontaneous velocity which corresponds to the velocity each individual would like to have in the absence of other people. The actual velocity is then computed as the projection of the spontaneous velocity onto the set of admissible velocities (i.e. velocities which do not violate the non-overlapping constraint). We describe here the...

The aim of this paper is to develop a crowd motion model designed to handle highly packed situations. The model we propose rests on two principles: we first define a spontaneous velocity which corresponds to the velocity each individual would like to have in the absence of other people. The actual velocity is then computed as the projection of the spontaneous velocity onto the set of admissible velocities (i.e. velocities which do not violate the non-overlapping constraint). We describe here...

In the paper some existence results for periodic boundary value problems for the ordinary differential equation of the second order in a Hilbert space are given. Under some auxiliary assumptions the set of solutions is compact and connected or it is convex.