  The boundary value problem is examined for the system of elliptic equations
of from $-\Delta u + A(x)u = 0 \quad\text{in} \Omega,$ where $A(x)$ is positive
semidefinite matrix on $\mathbb{R}^{{k}\times{k}},$ and $\frac{\partial
u}{\partial \nu}+g(u)=h(x) \quad\text{on} \partial\Omega$ It is assumed that
$g\in C(\mathbb{R}^{k},\mathbb{R}^{k})$ is a bounded function which may vanish
at infinity. The proofs are based on Leray-Schauder degree methods.
