Nehari's problem and competing species systems

By Monica Conti, S. Terracini, Gianmaria Verzini. 2002

183 citations recorded by the source corpus.

Subfields: Applied Mathematics, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/6e2e776bb74310db54119d0cddb4bd03026c2cc7

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Citations in the corpus

Radial Solutions and Phase Separation in a System of Two Coupled Schrödinger Equations (2008, unknown): “For a classical solution of (2.3), we have d dt E(u, v) = ∫ B (∇u∇ut + (u− u3 − βv2u)ut) dx+ ∫ B (∇v∇vt + (v − v3 − βu2v)vt) dx = ∫ B (−∆u+ u− u3 − βv2u)ut dx+ ∫ B (−∆v + v − v3 − βu2v)vt dx = − ∫ B [(ut)2 + (vt)2] dx,(2.5) hence E is strictly decreasing along non-constant trajectories t 7→ ϕt(u0,…”
Uniform Bounds for Strongly Competing Systems: The Optimal Lipschitz Case (2014, background): “1) when β → +∞ has firstly been studied in [11, 12] by Conti, Terracini and Verzini in the so-called focusing case ωi > 0: it has been shown that any sequence of minimizers of the energy functional associated to (1.”
Segregated and Synchronized Vector Solutions for Nonlinear Schrödinger Systems (2013, background): “Systems of nonlinear Schrödinger equations have been the subject of extensive mathematical studies in recent years, for example, [2–6,8–10,14,15,17,18,20,21, 24,25,29,30,34] and references therein.”
Existence and asymptotic behavior of sign-changing solutions for the nonlinear Schrödinger–Poisson system in $${\mathbb{R}^3}$$R3 (2015, methodology): “To show that the minimizer of the constrained problem is a sign-changing solution, inspired by [7,10], we take advantage of quantitative deformation lemma and degree theory.”
Symmetry of Solutions to Variational Problems for Nonlinear Elliptic Equations via Reflection Methods (2010, background): “In particular, nodal solutions play a key role in describing segregation phenomena in elliptic and parabolic systems with a competitive coupling [ 29 , 37, 38].”
Multipulse Phases in k-Mixtures of Bose–Einstein Condensates (2008, background): “This phenomenon, called “phase separation”, has been studied, starting from [4, 5], in the case of μi > 0 and in [3] in the case μi < 0, for least energy solutions in non necessarily symmetric bounded domains.”
Infinitely many positive solutions for nonlinear equations with non-symmetric potentials (2012, background): “Phase separation has been proved in several cases with constant potentials such as in the work [6, 17, 25, 36, 46, 47] as the coupling constant β tends to negative infinity.”