TY - JOUR
T1 - A Note On Deformation Argument For L2 Normalized Solutions Of Nonlinear Schrödinger Equations And Systems
AU - Ikoma, Norihisa
AU - Tanaka, Kazunaga
N1 - Funding Information:
The first author is partially supported by JSPS KAKENHI Grant No. JP16K17623, JP17H02851 and the second author is partially supported by JSPS KAKENHI Grant No. JP17H02855, JP16K13771, JP26247014, JP18KK0073, JP19H00644. Both authors are supported by NSFC-JSPS bilateral joint research project “Variational study of nonlinear PDEs”.
Publisher Copyright:
© 2020, Advances in Differential Equations. All Right Reserved.
PY - 2019/11
Y1 - 2019/11
N2 - Abstract. We study the existence of L2 normalized solutions for nonlinear Schrödinger equations and systems. Under new Palais-Smale type conditions, we develop new deformation arguments for the constrained functional on (Formula Presented). As applications, we give other proofs to the results of [5, 8, 22]. As to the results of [5, 22], our deformation result enables us to apply the genus theory directly to the corresponding functional to obtain infinitely many solutions. As to the result [8], via our deformation result, we can show the existence of vector solution without using constraint related to the Pohozaev identity.
AB - Abstract. We study the existence of L2 normalized solutions for nonlinear Schrödinger equations and systems. Under new Palais-Smale type conditions, we develop new deformation arguments for the constrained functional on (Formula Presented). As applications, we give other proofs to the results of [5, 8, 22]. As to the results of [5, 22], our deformation result enables us to apply the genus theory directly to the corresponding functional to obtain infinitely many solutions. As to the result [8], via our deformation result, we can show the existence of vector solution without using constraint related to the Pohozaev identity.
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M3 - Article
AN - SCOPUS:85083776916
SN - 1079-9389
VL - 24
SP - 609
EP - 646
JO - Advances in Differential Equations
JF - Advances in Differential Equations
IS - 11-12
ER -