NON-RADIAL GROUND STATES FOR THE HÉNON EQUATION

By D. Smets, Michel Willem, Jiabao Su. 2002

255 citations recorded by the source corpus.

Subfields: Computational Theory and Mathematics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/f790528f02f89ba17a67353d4efcf311e9c5212f

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Citations in the corpus

Non radial positive solutions for the Hénon equation with critical growth (2005, methodology): “cited above can in particular be seen as multiplicity results, in the sense that for α large problem (Pα) has at least two solutions: the radial one found by Ni (which survives when p ≥ 2∗) and the non radial ground state found in [10], which disappears when p = 2∗.”
Multiple Boundary Concentrating Solutions to Dirichlet Problem of Hénon Equation (2006, background): “The main idea used in [21] is to compare the energy of ground state solutions and that of radially symmetric solutions when ε > 0 is sufficiently small.”
Radial and non radial solutions for Hardy–Hénon type elliptic systems (2010, background): “2 The ground state level Following the ideas of Smetz, Su and Willem in [26], we give an upper bound for the level Sα,β = inf Wr ( )\{0} R(u) (26) Proposition 11 Let p, q as in (4), such that N p + 1 + N q + 1 > N − 2.”
Infinitely many nonradial solutions for the Hénon equation with critical growth (2013, background): “When N = 2, Smets–Su–Willem [13] showed that the mountain pass solution is nonradial when α is large.”
Positive radial solutions for Dirichlet problems with mean curvature operators in Minkowski space (2013, background): “Problems of this type have been widely studied (see for instance [23,24,27,29] and the references therein).”
Multiplicity Results for the Supercritical Hénon Equation (2004, background): “This is essentially the same estimate obtained in [9]; the proof in that paper however works only for p ≤ 2∗, while we are mainly interested in supercritical growths.”
On the Schrödinger–Poisson–Slater System: Behavior of Minimizers, Radial and Nonradial Cases (2009, background): “Nonradial ground states have been found in other frameworks previously, like in the Hénon equation, see [28].”
Uniqueness (2021, unknown): “…⊂ R N , with N ≥ 1, be the unit ball in R N centered at the origin and consider the H´enon equation [46] (2.3) Then the classical solutions of (2.3) are critical points of Let α > 0 be large enough such that least energy solutions —L.E.S. for short—of (2.3) are not radially symmetric; see [25,76].”
Hamiltonian elliptic systems: a guide to variational frameworks (2014, background): “6) the situation is more tricky since both the corresponding ground critical levels, the radial one and the global one, may grow asymptotically at the same rate, see [24], and this is in great contrast with the case of a single equation, as treated by [96].”
Non-radial Maximizers For Functionals With Exponential Non-linearity in ℝ2 (2005, background): “We also want to remark that in spite of these ”simmetry breaking phenomena” the maximizers may still present a weaker symmetry, as suggested in the paper of Smets and Willem [15].”
Lyapunov inequalities for partial differential equations (2006, methodology): “This has been used in the study of the existence of nonsymmetric ground states of symmetric problems for nonlinear PDE’s (see [1,2,11]).”
The asymptotic behaviour of the ground state solutions for Hénon equation (2003, background): “They have also studied the case when p is close to 2∗ in [20].”