# The intermediate solution of quasilinear elliptic boundary value problems

• Ko, Bong-Soo (Department of Mathematics Education Cheju National University)
• Published : 1994.08.01

#### Abstract

We study the existence of an intermediate solution of nonlinear elliptic boundary value problems (BVP) of the form $$(BVP) {\Delta u = f(x,u,\Delta u), in \Omega {Bu(x) = \phi(x), on \partial\Omega,$$ where $\Omega$ is a smooth bounded domain in $R^n, n \geq 1, and \partial\Omega \in C^{2,\alpha}, (0 < \alpha < 1), \Delta$ is the Laplacian operator, $\nabla u = (D_1u, D_2u, \cdots, D_nu)$ denotes the gradient of u and $$Bu(x) = p(x)u(x) + q(x)\frac{d\nu}{du} (x),$$ where $\frac{d\nu}{du} denotes the outward normal derivative of u on$\partial\Omega\$.