Partial symmetry of least energy nodal solutions to some variational problems

By Thomas Bartsch, Tobias Weth, Michel Willem. 2005

221 citations recorded by the source corpus.

Subfields: Applied Mathematics, Computational Theory and Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/df8271f7f57846327d712d9391d42b4d939b42c7

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

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 semilinear elliptic equations via Morse index (2007, result): “A first result, concerning variational problems where minimizers are sign changing functions, has been obtained recently in [3] where, using again symmetrization techniques, the authors extend the results of [13].”
Existence of groundstates for a class of nonlinear Choquard equations (2012, methodology): “[31] and the argument based on the Euler-Lagrange equation satisﬁed by polarizations [5,42].”
On the symmetry of minimizers (2007, methodology): “We have to mention that in a series of recent papers (see [2], [15], [17] and references therein), different new techniques were developed to study the symmetry of solutions for some classes of elliptic problems.”
Existence of Groundstates for a Class of Nonlinear Choquard Equations in the Plane (2016, methodology): “[24] M. Willem, Minimax theorems, Progress in Nonlinear Differential Equations and their Applications, 24, Birkhäuser, Boston, Mass., 1996.”
Desingularization of Vortices for the Euler Equation (2009, methodology): “It is a standard procedure [6–8,16] to prove that Proposition 5.”
Symmetry of Solutions to Variational Problems for Nonlinear Elliptic Equations via Reflection Methods (2010, background): “(i) The existence and foliated Schwarz symmetry of least energy nodal solutions has been established in a more general setting than considered here, see [12, 13 , 26, 63, 87] for details.”
Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics (2012, methodology): “Weth [4, 31], which consists in using the minimality property of the groundstate to deduce some relationship between the function and its polarization.”