TY - JOUR
T1 - Deformation Argument under PSP Condition and Applications
AU - Cingolani , Silvia
AU - Tanaka , Kazunaga
JO - Analysis in Theory and Applications
VL - 2
SP - 191
EP - 208
PY - 2021
DA - 2021/04
SN - 37
DO - http://doi.org/10.4208/ata.2021.pr80.03
UR - https://global-sci.org/intro/article_detail/ata/18771.html
KW - Deformation theory, nonlinear elliptic equations, radially symmetric solutions, strip-like domains, Pohozaev functional.
AB - <p style="text-align: justify;">In this paper we introduce a new deformation argument, in which $C^0$-group action and a new type of Palais-Smale condition PSP play important roles. This type of deformation results are studied in [17,21] and has many different applications [10, 11, 17, 21] et al. Typically it can be applied to nonlinear scalar field equations. We give a survey in an abstract functional setting. We also present another application to nonlinear elliptic problems in strip-like domains. Under conditions related to [5,6], we show the existence of infinitely many solutions. This extends the results in [8].</p>