Ground states of nonlinear Schrödinger equations with potentials

By Yongqing Li, Zhi-Qiang Wang, Jing Zeng. 2006

182 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/324b7a6eefae1628378c40c605e9514ff50475ea

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In Applied Mathematics

In Mathematical Physics

Citations in the corpus

A mass supercritical problem revisited (2020, methodology): “2) under the monotonicity condition (f4) is somehow inspired by the papers [25, 29, 33] where the authors demonstrated that under a Nehari type condition it is possible to find solutions without using the Ambrosetti-Rabinowitz condition.”
Elliptic Equations and Systems with Subcritical and Critical Exponential Growth Without the Ambrosetti–Rabinowitz Condition (2014, methodology): “It improves results of Miyagaki and Souto [32] to the (SCPI) growth and also gives a different approach from that of [28, 29].”
New conditions on nonlinearity for a periodic Schrödinger equation having zero as spectrum (2014, background): “There is a large literature on existence and multiplicity results, for example, [3,5–7,9–11,15–17,19–23,27,28,30,32,33].”
Existence of a positive solution to Kirchhoff type problems without compactness conditions (2012, background): “2 has been obtained by many authors, for example, [1,3,10,11,14].”
On ground states of superlinear p-Laplacian equations in RN (2010, methodology): “As in [ 19 ], we can also consider the potential well case.”
New Super-quadratic Conditions on Ground State Solutions for Superlinear Schrödinger Equation (2014, unknown): “(SQ) was first introduced by Liu and Wang [12] and then was commonly used in recent papers, see [4, 5, 6, 8, 9, 13, 14, 16, 20, 18, 23].”
Non-Nehari manifold method for asymptotically periodic Schrödinger equations (2014, methodology): “In the definite case where σ(−△+ V ) ⊂ (0,∞), Theorem 1.1 is a slight extension of a result by Li, Wang and Zeng [14].”
Wang’s multiplicity result for superlinear (,)–equations without the Ambrosetti–Rabinowitz condition (2013, methodology): “For an overview of the relevant literature in this direction, we refer to the pioneering papers of Liu–Wang [17] and of Li–Wang–Zeng [14] (where the analogue of H(ii) in Section 3 below was introduced for p = 2), and to the more recent ones of Li–Yang [15], Liu [16] and Miyagaki–Souto [19].”
N-Laplacian Equations in ℝN with Subcritical and Critical GrowthWithout the Ambrosetti-Rabinowitz Condition (2013, background): “Li, Wang and Zeng [34] also applied such a Nehari type argument to produce ground states of superlinear Schödinger equations whose nonlinearity does not satisfy (AR).”