Uniqueness of large positive solutions

General uniqueness results for large solutions

“…Naturally, ∂Ω satisfies the local graph property if it is Lipschitz continuous. Similarly, in order to avoid the use of the asymptotic expansions of the large solutions near the boundary in the proof of the uniqueness, another technique was introduced in [16], and later refined in [2] and [19], in a radially symmetric context, based on the strong maximum principle. This technique, which works out even in the context of cooperative systems, [18], will be combined in this paper with the technique of [22] in order to get the new findings of this paper.…”

Large solutions for cooperative logistic systems: existence and uniqueness in star-shaped domains

“…Then, (1) has a unique positive solution. [12] establishes the uniqueness of solution for the radially symmetric counterpart of (1) with constant coupling coefficients, a i j ∈ R + , 1 ≤ i = j ≤ n, while [15, Theorem 1.1] only deals with (1) in the restricted case n = 1 and a 11 ∈ R. On the other hand, the case where Ω is an annular region is covered in [12] and [15].…”