On the asymptotic behavior of solutions of certain elliptic type equations on noncompact Riemannian manifolds
The authors study the behavior of the bounded solutions of equations of the form \[ Lu=\Delta u-c(x) u=0\quad \text{ on} \;M, \] where \(c(x)\) is a smooth nonnegative function. Here \(M\) is a complete Riemannian manifold which can be represented as the union \(M=B\cap D,\) where \(B\) is a compact and \(D\) is isometric to the direct product \(R_+\times S\) (\(S\) is a compact Riemannian manifold). They discuss the solvability of the Dirichlet problem \[ \lim_{r\to\infty} u(r,\theta)=\Phi(\theta) \] for any continuous function \(\Phi(\theta)\) on \(S.\)
scientific article; zbMATH DE number 1541482