Soliton solutions for quasilinear Schrödinger equations, I
By Jiaquan Liu, Zhi-Qiang Wang. 2002
428 citations recorded by the source corpus.
Subfields: Applied Mathematics, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/20ea38c5cc1efbaacdf0856c0a8468f39afc8d47
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In Applied Mathematics
- Zhi-Qiang Wang
- Louis Jeanjean
- Tingjian Luo
- Xiangqing Liu
- Jiaquan Liu
- Olimpio Hiroshi Miyagaki
- A. Ambrosetti
- Gaetano Siciliano
In Mathematical Physics
- Zhi-Qiang Wang
- Louis Jeanjean
- Xiangqing Liu
- Tingjian Luo
- Jiaquan Liu
- A. Ambrosetti
- Olimpio Hiroshi Miyagaki
- Sérgio Henrique Monari Soares
Citations in the corpus
- Quasilinear elliptic equations via perturbation method (2012, methodology): “There have been several ideas and approaches used in recent years to overcome the difficulties such as by minimizations [13, 15], the Nehari method [12], and change of variables [7, 11].”
- Soliton solutions for quasilinear Schrodinger equations: the critical exponential case (2007, positive): “To overcome this difficulty, we employ an argument developed by Liu, Wang and Wang in [15] (see also [8, Lemma 2.1]).”
- Positive solutions to a class of quasilinear elliptic equations on R (2003, background): “Furthermore, setting as in the preceding Lemma vn = un − u, we claim that γ(u) + lim inf γ(vn) ≤ 0, (12) so that either γ(u) ≤ 0 or lim inf γ(vn) ≤ 0 (or both).”
- Quasilinear elliptic equations with critical growth via perturbation method (2013, methodology): “This idea was initially used in [10,23] for existence of solutions of subcritical problems.”
- Existence of ground states for a modified nonlinear Schrödinger equation (2009, background): “In [28] the higher dimension case is considered.”
- Positive solutions to a class of quasilinear elliptic equations on $\mathbb R$ (2003, background): “Though ground state solutions for (6) have been studied for higher space dimensions in [12, 13] there are difficulties to generalize Theorem 1.”
- Multiple Sign-Changing Solutions for Quasilinear Elliptic Equations via Perturbation Method (2014, methodology): “On the other hand, as observed in [21] the natural critical exponent for equation (1.”