A class of Adams-Fontana type inequalities and related functionals on manifolds

摘要

A class of Adams-Fontana type inequalities are established on compact Riemannian manifolds without boundary via the Young inequality together with the usual Adams-Fontana inequality (Comment Math Helv 68:415-454, 1993). As an application, a sequence of functionals are defined on manifolds, a sufficient condition on which the Palais-Smale condition holds is given and the existence of critical points of the functionals is also considered in the spirit of Adimurthi (Ann Scuola Norm Sup Pisa Cl Sci 17:393-413, 1990) and Adimurthi and Sandeep (Nonlinear Differ Equ Appl 13:585-603, 2007).