Semi-classical states of nonlinear Schrödinger equations: a variational reduction method

By Manuel del Pino, Patricio Felmer. 2002

211 citations recorded by the source corpus.

Subfields: Mathematical Physics, Numerical Analysis, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/0fe27d983ca5b9d9757e1c9bcfdbc18cfeba5a8e

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In Mathematical Physics

In Numerical Analysis

In Statistical and Nonlinear Physics

Citations in the corpus

Hamiltonian elliptic systems: a guide to variational frameworks (2014, background): “This was extended in [51] to find multiple spike solutions concentrating around a finite prescribed number of local minima of V , or around given topologically nontrivial critical points of V [48, 50].”
Groundstates for the nonlinear Schrödinger equation with potential vanishing at infinity (2010, unknown): “[7,8].”
Intermediate reduction method and infinitely many positive solutions of nonlinear Schrödinger equations with non-symmetric potentials (2015, background): “Assuming that d = 2R sin π K → +∞, as K → +∞, by the expansion (3.3), both positive numbers R and d are uniquely determined by K .”
Solutions of perturbed Schrödinger equations with critical nonlinearity (2007, methodology): “Without assumption of non-degeneracy on critical points of V, the existence of (positive) solutions was handled in Rabinowitz [21], del Pino and Felmer [9,10] and Jeanjean and Tanaka [15].”
Spikes in Two-component Systems of Nonlinear Schrodinger Equations with Trapping Potentials (2006, background): “We refer the reader for instance to [1, 3, 2, 4, 5, 8, 9, 10, 12, 14, 15, 16, 17, 18, 22, 23, 25, 26] and the references therein.”
Semi-classical standing waves for nonlinear Schrödinger equations at structurally stable critical points of the potential (2013, methodology): “The authors would like to express their sincere thanks to Paul Rabinowitz, Norman Dancer, Manuel del Pino, Patricio Felmer and Louis Jeanjean for their helpful comments and fruitful discussions during the preparation of this paper.”
Solutions with multiple spike patterns for an elliptic system (2007, background): “1) the analog of the results in [13,15] concerning a single equation.”
Existence and Concentration Result for the Kirchhoff Type Equations with General Nonlinearities (2014, unknown): “For instance, we refer to [5–7,20,21,25– 27,33,44,48,54,55].”
Standing Waves for Nonlinear Schrödinger Equations with a General Nonlinearity: One and Two Dimensional Cases (2008, methodology): “In a different direction, a variational approach was initiated by Rabinowitz (1992) and developed further by several authors (see Byeon and Wang, 2002, 2003; Cingolani and Lazzo, 2000; Cingolani and Nolasco, 1998; Del Pino and Felmer, 1996, 1997, 1998, 2002; Gui, 1996; Jeanjean and Tanaka, 2004).”