A simple variational approach to weakly coupled competitive elliptic systems

Weakly Coupled Elliptic Systems and Positivity

In this paper we will study under which conditions the positive cone, or part of the positive cone, is preserved when solving a weakly coupled system of elliptic partial differential equations. Such a system will be as follows:  −∆1 0 0 . . . 0 0 −∆k   u1 .. uk  =  c11 · · · c1k .. .. ck1 · · · ckk   u1 .. uk +  f1 .. fk  on a bounded domain in IR, with zero Dirichlet bounda...

A Variational Approach to Estimating Uncertain Parameters in Elliptic Systems

Harnack’s Inequality for Cooperative Weakly Coupled Elliptic Systems

A bstract . We consider cooperative, uniformly elliptic systems, with bounded coefficients and coupling in the zeroth-order terms. We establish two analogues of Harnack’s inequality for this class of systems: A weak version is obtained under fairly general conditions, while imposing an irreducibility condition on the coupling coefficients we obtain a stronger version of the inequality. This irr...

Monotone Difference Schemes for Weakly Coupled Elliptic and Parabolic Systems

The present paper is devoted to the development of the theory of monotone difference schemes, approximating the so-called weakly coupled system of linear elliptic and quasilinear parabolic equations. Similarly to the scalar case, the canonical form of the vector-difference schemes is introduced and the definition of its monotonicity is given. This definition is closely associated with the prope...

Some local fixed point results under $C$-class functions with applications to coupled elliptic systems

The main objective of the paper is to state newly fixed point theorems for set-valued mappings in the framework of 0-complete partial metric spaces which speak about a location of a fixed point with respect to an initial value of the set-valued mapping by using some $C$-class functions. The results proved herein generalize, modify and unify some recent results of the existing literature. As an ...