THE EXISTENCE OF SOLUTIONS OF NONLINEAR BOUNDARY VALUE PROBLEMS INVOLVING THE p-LAPLACIAN OPERATOR IN L~s-SPACES

By using the perturbation theories on sums of ranges of nonlinear accretive mappings of Calvert and Gupta, we study the abstract results on the existence of a solution u ∈ LS(Ω) of nonlinear boundary value problems involving the p-Laplacian operator, where 2 ≤ s +∞, and 2N/N+1 p ≤ 2 for N(≥ 1) which denotes the dimension of RN. To obtain the result, some new techniques are used in this paper. The equation discussed in this paper and our methods here are extension and complement to the corresponding results of L. Wei and Z. He.