The author considers semilinear elliptic boundary value problems of the form \[ (*)\quad Lu:=-\sum^{N}_{i,j=1}D_ i(a_{ij}(x)D_ ju)=f(x,u,\nabla u)\quad in\quad \Omega, \]
\[ Bu:=\sum^{N}_{i,j=1}a_{ij}(x)\cos (\nu,x_ j)D_ iu+h(x)u=g(x,u)\quad on\quad \partial \Omega, \] where \(\Omega\) is an exterior domain in \({\mathbb{R}}^ N\), \(\nu\) the outer normal vector to \(\Omega\) at x.
In a recent paper [see the author, Funkc. Ekvacioj, Ser. Int. 27, 281-289 (1984; Zbl 0575.35031)] he obtained results concerning the existence and multiplicity theory of bounded solutions of (*) in case when f and g are convex in u, \(\nabla u\) respectively u. In this paper the author studies the multiplicity of positive solutions of (*), when f and g are sublinear. Sublinearity: If for all \(\alpha\in [0,1]\), \(s\in {\mathbb{R}}^+\), \(t\in {\mathbb{R}}^ N\) \[ f(x,\alpha s,\alpha t)\geq \alpha f(x,s,t),\quad g(x,\alpha s)\geq \alpha g(x,s)\quad on\quad \Omega. \] The author constructs a nonlinear operator equation whose fixed points are solutions of (*).