Solutions to indefinite weakly coupled cooperative 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...

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...

Infinitely Many Solutions of Strongly Indefinite Semilinear Elliptic Systems

Convergence rate of approximate solutions to weakly coupled nonlinear systems

We study the convergence rate of approximate solutions to nonlinear hyperbolic systems which are weakly coupled through linear source terms. Such weakly coupled 2 × 2 systems appear, for example, in the context of resonant waves in gas dynamics equations. This work is an extension of our previous scalar analysis. This analysis asserts that a One Sided Lipschitz Condition (OSLC, or Lip-stability...

Existence of Solutions for a Class of Weakly Coupled Semilinear Elliptic Systems

where A is the m-component Laplacian. In what follows it shall be convenient to use both formulations. We hope that our use of both vector and component notation shall not lead to confusion. Speaking in the roughest possible terms we employ the properties of a convex function H to control the growth of the reaction vector field f: This in turn allows the use of a scalar comparison function to d...