Symmetry Results for Semilinear Elliptic Systems in the Whole Space

By J. Busca, Boyan Sirakov. 2000

222 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics

View Paper: https://www.semanticscholar.org/paper/f71805cde0fb999164b78c1507e22384d4e21ab0

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

In Applied Mathematics

In Computational Theory and Mathematics

Citations in the corpus

Uniqueness of positive solutions to some coupled nonlinear Schrödinger equations (2011, background): “In this paper, we concentrate on the attractive case, i.e. β > 0.”
Bound states for a coupled Schrödinger system (2007, background): “In fact, due to the work of Busca and Sirakov [8], solutions of (1.”
Uniqueness of Positive Solutions for a Nonlinear Elliptic System (2009, methodology): “These inequalities are corresponding to the inequality (13) in [2] and we can show (22) in a similar way to [2].”
Minimal energy solutions for cooperative nonlinear Schrödinger systems (2015, result): “Hence, the symmetry results of Busca and Sirakov [3] and Ikoma [7] imply the radial symmetry and monotonicity of the functions u, v. Similarly, using Proposition 1, one shows that minimizers of I|Mb are radially symmetric and do not change sign.”
Hamiltonian elliptic systems: a guide to variational frameworks (2014, background): “1) by Troy [104], see also [29, 42, 93] and Remark 3.”
On cooperative parabolic systems: Harnack inequalities and asymptotic symmetry (2009, result): “Da Lio and Sirakov [17] considered an even more general class of elliptic equations, including equations involving Pucci operators, and they proved the symmetry of positive viscosity solutions.”
Positive solutions for a weakly coupled nonlinear Schrödinger system (2006, unknown): “If u and v are both nontrivial functions, the strong maximum principle implies that they are positive functions, so we apply the result of [14] to deduce that u and v are radial functions (up to translations) and that decay to zero exponentially as |x| → +∞.”
Multiple positive normalized solutions for nonlinear Schrödinger systems (2017, background): “1) where (λ1,λ2) are given has been, starting from the pioneering papers [2, 13, 27, 30, 36], the subject of a huge literature in the recent years.”
Liouville type theorems, monotonicity results and a priori bounds for positive solutions of elliptic systems (2005, methodology): “We use this fact as in the proof of Theorem 2 from [11] (see hypotheses (i)–(iii) in Section 2.”
Least Energy Solitary Waves for a System of Nonlinear Schrödinger Equations in $${\mathbb{R}^n}$$ (2007, background): “Remark 3. If β ≥ 0 then any nonstandard nonnegative solution of (4) is strictly positive and radial, by the strong maximum principle and the results in [ 5 ], see Sect.”
Solutions with multiple spike patterns for an elliptic system (2007, background): “We know from [4] that u and v are radially symmetric with respect to the origin and that they are decreasing functions.”
Semiclassical states for weakly coupled nonlinear Schrödinger systems (2008, background): “The sequence(φn, ψn) C2 converges over compact sets to a least energy solution(φz, ψz) of (Sz), andφz, ψz are radially and exponentially decaying (see [10]), that is,(φz, ψz) belongs toS(z).”