ON EXISTENCE OF WEAK SOLUTIONS OF NEUMANN PROBLEM FOR QUASILINEAR ELLIPTIC EQUATIONS INVOLVING p-LAPLACIAN IN AN UNBOUNDED DOMAIN

In this paper we study the existence of non-trivial weak solutions of the Neumann problem for quasilinear elliptic equations in the form -div(h(x)|∇ u|^(p-2)∇ u)+b(x)|u|^(p-2)u= f(x,u) , p≥2 in an unbounded domain Ω ⊂ R^N, N≥ 3, with sufficiently smooth bounded boundary ∂Ω, where h(x) ∈ [수식], [기호]=Ω∪∂Ω, h(x)≥ 1 for all x ∈Ω. The proof of main results rely essentially on the arguments of variational method. KCI Citation Count: 3