Standing Waves with a Critical Frequency for Nonlinear Schrödinger Equations

By Jaeyoung Byeon, Zhi-Qiang Wang. 2002

309 citations recorded by the source corpus.

Subfields: Atomic and Molecular Physics, and Optics, Mathematical Physics, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/9c68a15a79dab42f49c8628d0833ff50034c8b2e

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In Atomic and Molecular Physics, and Optics

In Mathematical Physics

In Statistical and Nonlinear Physics

Citations in the corpus

On the Mass Concentration for Bose–Einstein Condensates with Attractive Interactions (2013, background): “16) as h → 0, see [13, 33, 37, 7] and references therein.”
Standing Waves for Nonlinear Schrödinger Equations with a General Nonlinearity: One and Two Dimensional Cases (2008, methodology): “For the physical background of this equation, we refer to the introduction in [8].”
Semi-classical states for the Choquard equation (2013, unknown): “Such solutions were constructed for the local nonlinear Schrödinger equation [14,15].”
Semiclassical states for nonlinear Schrödinger equations with sign-changing potentials (2007, result): “Among the results, Byeon and Wang [5] considered the case with g(u) independent of x, and Ding and Lin [8] handled the case with g(x,u) is of critically growth.”
Choquard-type equations with Hardy–Littlewood–Sobolev upper-critical growth (2018, background): “The functional Qε that was first introduced in [13] will act as a penalization to forcing the concentration phenomena inside O.”
On the multiplicity of solutions of a nonlinear elliptic problem on Riemannian manifolds (2007, background): “We limit ourselves to citing [1–3,5–7,9], and refer to references therein.”
Solutions with multiple spike patterns for an elliptic system (2007, background): “In [5] the function V is allowed to vanish at some points of RN .”
Superlinear Schrödinger–Kirchhoff type problems involving the fractional p–Laplacian and critical exponent (2019, background): “In [37], Byeon and Wang rst studied the asymptotic behavior of positive solutions to Schrodinger equations under the condition infx∈RN V(x) = 0, which is called critical frequency.”
The toda system and multiple-end solutions of autonomous planar elliptic problems (2007, background): “We refer the reader to [2, 3, 7, 11, 12, 13, 16, 20, 21, 27, 29, 30, 39, 37, 38] and references therein.”
Concentration on curves for nonlinear Schrödinger Equations (2007, background): “We refer the readerfor instanceto [2], [4], [7]-[13], [15, 16, 17, 18, 21, 31, 32, 34, 36, 37, 38].”
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.”
Standing waves with a critical frequency for nonlinear Schrödinger equations, II (2003, background): “Ground state solutions have been studied in [ 10 ] where we have shown that there exists a ground state solution concentrating near an isolated component of the zero set of V for f (v )= v p with 2 <p +1 < 2 ∗ . Here 2 ∗ = 2N”