Nonhomogeneous fractional pp-Kirchhoff problems involving a critical nonlinearity

摘要

This paper is concerned with the existence of solutions for a kind of nonhomogeneous critical pp-Kirchhoff type problem driven by an integro-differential operator LpKLKp. In particular, we investigate the equation: M(?R2n|v(x)?v(y)|p|x?y|n+psdxdy)LpKv(x)=μg(x)|v|q?2v+|v|p?s?2v+μf(x)in Rn, M(?R2n|v(x)?v(y)|p|x?y|n+psdxdy)LKpv(x)=μg(x)|v|q?2v+|v|ps??2v+μf(x)in Rn, where g(x)>0g(x)>0, and f(x)f(x) may change sign, μ>0μ>0 is a real parameter, 0ps, 1