Existence of Quermass-Interaction Process for non locally stable interaction and non bounded convex grains

Quermass-interaction Processes: Conditions for Stability

We consider a class of random point and germ-grain processes, obtained using a rather natural weighting procedure. Given a Poisson point process, on each point one places a grain, a (possibly random) compact convex set. Let be the union of all grains. One can now construct new processes whose density is derived from an exponential of a linear combination of quermass functionals of. If only the ...

Best proximity point theorems in Hadamard spaces using relatively asymptotic center

In this article we survey the existence of best proximity points for a class of non-self mappings which‎ satisfy a particular nonexpansiveness condition. In this way, we improve and extend a main result of Abkar and Gabeleh [‎A‎. ‎Abkar‎, ‎M‎. ‎Gabeleh‎, Best proximity points of non-self mappings‎, ‎Top‎, ‎21, (2013)‎, ‎287-295]‎ which guarantees the existence of best proximity points for nonex...

Continuum percolation for quermass interaction model

Continuum percolation for Markov (or Gibbs) germ-grain models in dimension 2 is investigated. The grains are assumed circular with random radii on a compact support. The morphological interaction is the so-called Quermass interaction defined by a linear combination of the classical Minkowski functionals (area, perimeter and Euler-Poincaré characteristic). We show that percolation occurs for any...

Some Results on Boundedness in Locally Convex Cones

The Solvability of Concave-Convex Quasilinear Elliptic Systems Involving $p$-Laplacian and Critical Sobolev Exponent

In this work, we study the existence of non-trivial multiple solutions for a class of quasilinear elliptic systems equipped with concave-convex nonlinearities and critical growth terms in bounded domains. By using the variational method, especially Nehari manifold and Palais-Smale condition, we prove the existence and multiplicity results of positive solutions.