Global minimizers of coexistence for competing species

Conti, Monica; Felli, Veronica

doi:10.1112/jlms/jdq085

Cited by 5 publications

(2 citation statements)

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“…In particular, we find that the supports of u b , v b separate as b → −∞. In general bounded domains Ω ⊂ R n these phenomena have been extensively studied in [3], [4], [5], [13] and our Theorem 1 can be considered as one kind of extension of their results.…”

Section: Introductionmentioning

confidence: 64%

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Minimal energy solutions for repulsive nonlinear Schrödinger systems

Mandel

2014

Journal of Differential Equations

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In this paper we establish existence and nonexistence results concerning fully nontrivial minimal energy solutions of the nonlinear Schrödinger systemWe consider the repulsive case b < 0 and assume that the exponent q satisfies 1 < q < n n−2 in case n ≥ 3 and 1 < q < ∞ in case n = 1 or n = 2. For space dimensions n ≥ 2 and arbitrary b < 0 we prove the existence of fully nontrivial nonnegative solutions which converge to a solution of some optimal partition problem as b → −∞. In case n = 1 we prove that minimal energy solutions exist provided the coupling parameter b has small absolute value whereas fully nontrivial solutions do not exist if 1 < q ≤ 2 and b has large absolute value.

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Section: Introductionmentioning

confidence: 64%

“…Its proof is given in four steps. First we prove variational characterizations for the values κ * b , κ * −∞ which turn out to be more convenient than the original ones given by (2) and (4). In the second step we use these characterizations to prove that minimizers of the functionals I| M * b and I| M * −∞ exist.…”

Section: Proof Of Theoremmentioning

confidence: 99%