| Full text | |
| Author(s): |
Nornberg, Gabrielle
;
Schiera, Delia
;
Sirakov, Boyan
Total Authors: 3
|
| Document type: | Journal article |
| Source: | DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS; v. 40, n. 6, p. 25-pg., 2020-06-01. |
| Abstract | |
We consider fully nonlinear uniformly elliptic cooperative systems with quadratic growth in the gradient, such as -F-i(x, u(i), Du(i), D(2)u(i)) - < M-i(x) Du(i), Du(i)> = lambda c(i1)(x)u(1 )+...+ lambda c(in)(x) u(n) + h(i)(x), for i = 1, ..., n, in a bounded C-1,C-1 domain Omega subset of R-N with Dirichlet boundary conditions; here n >= 1, lambda is an element of R, c(ij) , h(i) is an element of L-infinity (Omega), c(ij) >= 0, M-i , satisfies 0 < mu I-1 <= M-i <= mu I-2, and F-i is an uniformly elliptic Isaacs operator. We obtain uniform a priori bounds for systems, under a weak coupling hypothesis that seems to be optimal. As an application, we also establish existence and multiplicity results for these systems, including a branch of solutions which is new even in the scalar case. (AU) | |
| FAPESP's process: | 18/04000-9 - EXISTENCE AND MULTIPLICITY OF SOLUTIONS FOR ELLIPTIC PROBLEMS WITH QUADRATIC GROWTH IN THE GRADIENT |
| Grantee: | Gabrielle Saller Nornberg |
| Support Opportunities: | Scholarships in Brazil - Post-Doctoral |