We consider the following equation \(\bigtriangleup u(x)+F(x,u(x),v(x))+g(x)x\cdot \nabla u(x)=0,\) for \(x\in \Omega _{R}=\left\{ x\in \mathbb {R}^{n},||x||>R\right\} ,\) \(n>2\) with the condition \(u(x)=\Theta (||x||^{2-n})\) as \(||x||\rightarrow +\infty .\) The goal of the paper is to discuss the existence of minimal solutions of a class of elliptic problems and their dependence on functional parameters from a subset V of a certain Hölder space. The latter result will be obtained in the case of the lack of uniqueness of a solution. We will show that for each parameter from V, our problem possesses a non-decreasing sequence of minimal solutions with finite energy.
