Multiple Positive Solutions to Nonlinear Schrödinger Equations with Competing Potential Functions

By Silvia Cingolani, M. Lazzo. 2000

267 citations recorded by the source corpus.

Subfields: Applied Mathematics, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/567f9bd3ebbaed7ae3871972c26b2ea01065e1b0

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Citations in the corpus

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.”
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).”
Multiplicity and concentration behavior of positive solutions for a Schrödinger–Kirchhoff type problem via penalization method (2013, methodology): “1) have been extensively studied in recent years, see for example the papers [7, 8, 11, 12, 15, 24] and their references.”
Existence and concentration of positive ground states for a Kirchhoff equation involving critical Sobolev exponent (2014, methodology): “As we known, this kind of hypothesis has been introduced by Wang and Zeng [44], Cingolani and Lazzo [12] and Zhao and Zhao [47] in the study of nonlinear Schrödinger and Schrödinger-Possion system.”
Concentration on curves for nonlinear Schrödinger Equations (2007, background): “We refer the reader, for instance, to [2, 4, 7, 8, 9, 10, 11, 12, 13, 15, 16, 17, 18, 22, 31, 32, 34, 36, 37, 38].”
Uniqueness of positive bound states with multi-bump for nonlinear Schrödinger equations (2015, background): “For other results concerning the existence of the solutions with the concentration phenomena, one can refer to [2, 3, 5, 11, 14, 16, 19, 23, 24, 26] and the references therein.”
Singularly perturbed critical Choquard equations (2016, background): “Cingolani and Lazzo [10] obtained a multiplicity result involving the set of global minima of a function which provides some kind of global median value between the minimum of V and the maximum ofK and Q.”
Existence and multiplicity of positive solutions to a $p$-Laplacian equation in $\Bbb R^N$ (2006, background): “[8] S. Cingolani and M. Lazzo, Multiple semiclassical standing waves for a class of nonlinear Schrödinger equations, Topol.”
Multiplicity Results for some Nonlinear¶Schrödinger Equations with Potentials (2000, unknown): “Let us also point out that the class of nonlinearities handled in [ 6 ] does not even require that (40) has a unique solution.”