Sublinear elliptic equations in \(\mathbb{R}{}^ n\). (English) Zbl 0761.35027

The main result is \(-\Delta u=\rho(x)u^ \alpha\), \(0<\alpha<1\), \(\rho\geq 0\), \(0\not\equiv\rho\in L^ \infty_{loc}\) has a bounded solution in \(\mathbb{R}^ n\), \(n\geq 3\), if and only if \(\rho\) satisfies property \((H)\), i.e. \(\Delta u=\rho\) in \(\mathbb{R}^ n\) has a bounded solution. Moreover there is a minimal positive solution of (1). Uniqueness results are established.
Reviewer: J.Frehse (Bonn)


35J60 Nonlinear elliptic equations
35B35 Stability in context of PDEs
35J05 Laplace operator, Helmholtz equation (reduced wave equation), Poisson equation
35B50 Maximum principles in context of PDEs
35B40 Asymptotic behavior of solutions to PDEs
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