We establish the existence of a nonnegative fully nontrivial solution to non-variational weakly coupled competitive elliptic system. show that this kind solutions belong topological manifold Nehari-type, and apply degree-theoretical argument on derive existence.

In this paper, we study a conjecture of J.Serrin and give a partial generalized result of the work of de Figueiredo and Felmer about Liouville type Theorem for non-negative solutions for an elliptic system. We use a new type of moving plane method introduced by Chen-Li-Ou. Our new ingredient is the use of Stein-Weiss inequality.

A virtual internal bond (VIB) model is proposed recently in mechanical engineering literatures for simulating dynamic fracture. The model is a nonlinear wave equation of mixed type (hyperbolic or elliptic). There is instability in the elliptic region and usual numerical methods might not work. We examine the artificial viscosity method for the model and apply central type schemes directly to th...

x.1. Elliptic Surfaces Deenition. An elliptic surface consists of a smooth (projective) surface E, a smooth (projective) curve C, and a morphism : E ?! C such that almost all bers E t = ?1 (t) are (smooth projective) curves of genus 1. In addition, we will generally assume that our elliptic surfaces come equipped with an identity section 0 : C ?! E which serves as the identity element of the gr...

Simply connected compact Kähler manifolds of dimension up to three with elliptic homotopy type are characterized in terms of their Hodge diamonds. This is applied to classify the simply connected Kähler surfaces and Fano threefolds with elliptic homotopy type.