TY - JOUR
T1 - Existence and asymptotic behavior of positive solutions for a class of locally superlinear Schrödinger equation
AU - Adachi, Shinji
AU - Ikoma, Norihisa
AU - Watanabe, Tatsuya
N1 - Funding Information:
This work was supported by JSPS KAKENHI Grant Numbers JP19K03590, JP19H01797, JP18K03362, JP21K03317 and by JSPS-NSFC joint research project “Variational study of nonlinear PDEs" and by the Research Institute for Mathematical Sciences, an International Joint Usage/Research Center located in Kyoto University.
Publisher Copyright:
© 2022, The Author(s), under exclusive licence to Springer-Verlag GmbH Germany, part of Springer Nature.
PY - 2022
Y1 - 2022
N2 - This paper treats the existence of positive solutions of - Δ u+ V(x) u= λ f(u) in RN. Here N≥ 1 , λ > 0 is a parameter and f(u) satisfies conditions only in a neighborhood of u= 0. We shall show the existence of positive solutions with potential of trapping type or G-symmetric potential where G⊂ O(N). Our results extend previous results (Adachi and Watanabe in J Math Anal Appl 507:125765, 2022; Costa and Wang in Proc Am Math Soc 133(3):787–794, 2005; do Ó et al. in J Math Anal Appl 342:432–445, 2008) as well as we also study the asymptotic behavior of a family (uλ)λ≥λ0 of positive solutions as λ → ∞.
AB - This paper treats the existence of positive solutions of - Δ u+ V(x) u= λ f(u) in RN. Here N≥ 1 , λ > 0 is a parameter and f(u) satisfies conditions only in a neighborhood of u= 0. We shall show the existence of positive solutions with potential of trapping type or G-symmetric potential where G⊂ O(N). Our results extend previous results (Adachi and Watanabe in J Math Anal Appl 507:125765, 2022; Costa and Wang in Proc Am Math Soc 133(3):787–794, 2005; do Ó et al. in J Math Anal Appl 342:432–445, 2008) as well as we also study the asymptotic behavior of a family (uλ)λ≥λ0 of positive solutions as λ → ∞.
UR - http://www.scopus.com/inward/record.url?scp=85140269131&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85140269131&partnerID=8YFLogxK
U2 - 10.1007/s00229-022-01428-5
DO - 10.1007/s00229-022-01428-5
M3 - Article
AN - SCOPUS:85140269131
JO - Manuscripta Mathematica
JF - Manuscripta Mathematica
SN - 0025-2611
ER -