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

Abstract

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).