Study on the Existence and Uniqueness of Solution of Generalized Capillarity Problem

Abstract

By using the perturbation theories on sums of ranges of nonlinear accretive mappings of Calvert and Gupta (1978), the abstract result on the existence and uniqueness of the solution in $L^p(\mathrm{\Omega })$ of the generalized Capillarity equation with nonlinear Neumann boundary value conditions, where and $N\left(\ge 1\right)$ denotes the dimension of $R^N$, is studied. The equation discussed in this paper and the methods here are a continuation of and a complement to the previous corresponding results. To obtain the results, some new techniques are used in this paper.