Concentration on curves for nonlinear Schrödinger Equations

By Manuel del Pino, M. Kowalczyk, Jun-cheng Wei. 2007

198 citations recorded by the source corpus.

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

View Paper: https://www.semanticscholar.org/paper/be35f0692c68cd0f55ce29286a1e9fdcfd13ac8f

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In Applied Mathematics

In Computational Theory and Mathematics

In Mathematical Physics

Citations in the corpus

Concentrating standing waves for the fractional nonlinear Schr\"odinger equation (2013, background): “See [11, 23] for concentration along a curve in the plane and s = 1.”
Some new entire solutions of semilinear elliptic equations on Rn (2009, result): “Existence of such solutions was shown in [3], [4], [6], [9] under some symmetry assumptions, and then in [ 18 ] the authors proved concentration along curves for n = 2 (see also [38], [39] for general n), in a non-symmetric setting.”
Green's function and infinite-time bubbling in the critical nonlinear heat equation (2016, methodology): “The inner-outer gluing technique has been a very useful tool in finding solutions for singular perturbation elliptic problems with higher dimensional concentration set, as developed in [8, 7, 9].”
The toda system and multiple-end solutions of autonomous planar elliptic problems (2007, unknown): “We refer the reader to [2, 3, 7, 11, 12, 13 , 16, 20, 21, 27, 29, 30, 39, 37, 38] and references therein.”
Concentration phenomenon for fractional nonlinear Schr\"{o}dinger equations (2013, background): “We limit ourselves to citing a few recent papers [3, 4, 6, 7, 28, 10, 42, 53, 29], referring to their bibliography for a broader list of works, although still not exhaustive.”
Intermediate reduction method and infinitely many positive solutions of nonlinear Schrödinger equations with non-symmetric potentials (2015, methodology): “Inspired by the results in [3, 21, 33, 41] and [34, 8], it is interesting to ask the following question:”
The Toda System and Clustering Interfaces in the Allen–Cahn equation (2008, methodology): “This will be done using a gluing procedure similar to that in [12].”
Semi-classical standing waves for nonlinear Schrödinger equations at structurally stable critical points of the potential (2013, methodology): “Even though there is such a restriction on the nonlinearity when we apply the reduction method, the Lyapunov–Schmidt reduction method is a very powerful tool when we construct very subtle (highly unstable) solutions with continuum peaks as we can see in [19].”