We discuss existence and classification of totally umbilic surfaces in the model geometries of Thurston and the Berger spheres. We classify such surfaces in H × R, S × R and the Sol group. We prove nonexistence in the Berger spheres and in the remaining model geometries other than the space forms.

In this paper, we consider pursuit-evasion and probabilistic consequences of some geometric notions for bounded and suitably regular domains in Euclidean space that are CAT(κ) for some κ > 0. These geometric notions are useful for analyzing the related problems of (a) existence/nonexistence of successful evasion strategies for the Man in Lion and Man problems, and (b) existence/nonexistence of ...

Sophisticated voting on a binary tree is a common form of voting structure, as exemplified by, for example, amendment procedures. The problem of characterizing voting rules that can be the outcome of this procedure has been a longstanding problem in social choice. We explore rules over a small number of candidates, and discuss existence and nonexistence properties of rules implementable over tr...

We consider the (n, p) boundary value problem in this paper. Some new upper estimates to positive solutions for the problem are obtained. Existence and nonexistence results for positive solutions of the problem are obtained by using the Krasnosel’skii fixed point theorem. An example is included to illustrate the results.

This paper is concerned with traveling wavefronts in a LotkaVolterra model with nonlocal delays for two cooperative species. By using comparison principle, some existence and nonexistence results are obtained. If the wave speed is larger than a threshold which can be formulated in terms of basic parameters, we prove the asymptotic stability of traveling wavefronts by the spectral analysis metho...

For a semilinear biharmonic Dirichlet problem in the ball with supercritical power-type nonlinearity, we study existence/nonexistence, regularity and stability of radial positive minimal solutions. Moreover, qualitative properties, and in particular the precise asymptotic behaviour near x = 0 for (possibly existing) singular radial solutions, are deduced. Dynamical systems arguments and a suita...

We study the Nehari manifold for a class of quasilinear elliptic systems involving a pair of (p,q)-Laplacian operators and a parameter. We prove the existence of a nonnegative nonsemitrivial solution for the systems by discussing properties of the Nehari manifold, and so global bifurcation results are obtained. Thanks to Picone’s identity, we also prove a nonexistence result.