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 -

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].