The Existence Of Solutions For A Class Of Quasilinear Elliptic Equations(Systems)

Fist of all, we are concerned with the quasilinear elliptic equations with concave and convex terms where Ω C RN is a bounded smooth domain,1<p<2,4<g≤22*,α,β∈R are parameters. Second, we considered the following quasilinear elliptic equations where Di=(?)/(?)xij and Ds∝ij(x,s)=(?)/(?)s(x,s). We prove the existence of multiple solutions for the above problems via the perturbation methods.Finally, we study the following periodic superlinear elliptic systems existence of a ground state solution is obtained by proving all Cerami sequence for the energy functional are bounded.