| Abstrakt: |
We deal with a coupled system of fc-Hessian equations: Sk (μ(D²u1)) = -u2)α in B, Sk (μ(D²u2)) = -u1)β in B, u1 < 0, u2 < 0 in B, u1 = u2 = 0 on ∂B, where k = 1,2, ..., TV, B is a unit ball in ℝN, N ≥ 2, α and β are positive constants. By using the fixed-point index theory in cone, we obtain the existence, uniqueness and nonexistence of radial convex solutions for some suitable constants α and β. Furthermore, by using a generalized Krein-Rutman theorem, we also obtain a necessary and sufficient existence condition of the convex solutions to a nonlinear eigenvalue problem. [ABSTRACT FROM AUTHOR] |
