The Neumann boundary value problem of higher order quasilinear elliptic equation

This paper is concerned with the generalized solution to the Neumann boundary value problem of higher order quasilinear elliptic equation: {∑1≤|α|≤m(−1)|α|DαAα(x,ξm(u))=f(x,u),x∈Ω,B(x,ξm(u))⋅ν=g(x,u),x∈∂Ω. We show that there exists at least one non-trivial solution for the above problem in Wm,p(x)(Ω)Wm,p(x)(Ω).