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

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... [5, 6] , we show the existence of infinitely many solutions. This extends the results in [8] .