The Neumann boundary value problem of higher order quasilinear elliptic equation Original Research Article

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