On Local Weak Solutions for Fractional in Time SOBOLEV-Type Inequalities

摘要

We consider two fractional in time nonlinear Sobolev-type inequalities involving potential terms, where the fractional derivatives are defined in the sense of Caputo. For both problems, we study the existence and nonexistence of nontrivial local weak solutions. Namely, we show that there exists a critical exponent according to which we have existence or nonexistence.