Multiple solutions to weakly coupled supercritical elliptic systems
نویسندگان
چکیده
منابع مشابه
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...
متن کاملConvergence 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...
متن کاملExistence 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...
متن کاملHarnack’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...
متن کاملMonotone 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...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Annali di Matematica Pura ed Applicata (1923 -)
سال: 2019
ISSN: 0373-3114,1618-1891
DOI: 10.1007/s10231-018-0820-2