Study on the existence and uniqueness of solution of generalized capillarity problem (Q1938122)

Summary: By using the perturbation theories on sums of ranges of nonlinear accretive mappings of \textit{B. D. Calvert} and \textit{C. P. Gupta} [Nonlinear Anal., Theory, Methods Appl. 2, No. 1, 1--26 (1978; Zbl 0369.47033)], the abstract result on the existence and uniqueness of the solution in \(L^p(\Omega)\) of the generalized capillarity equation with nonlinear Neumann boundary value conditions, where \(2N/(N + 1) < p < +\infty\) and \(N(\geq 1)\) denotes the dimension of \(\mathbb{R}^N\), 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.