Critical Elliptic Equations on Non-Compact Finsler Manifolds

In the present paper we deal with a quasilinear elliptic equation involvinga critical Sobolev exponent on non-compact Finsler manifolds, i.e. Randers spaces. Under very general assumptions perturbation prove existence of non-trivial solution. The approach is based direct methods calculus variations. One key step to that energy functional associated problem weakly lower semicontinuous small balls space, which provided by inequality. At end, Hardy-type inequalities manifolds as an application this