# zbMATH — the first resource for mathematics

On the elliptic equation $$D_ i[a_{ij}(x)D_ jU]-k(x)U+K(x)U^ p=0$$. (English) Zbl 0584.35031
The author studies entire, positive solutions of the equation $(1)\quad D_ i[a_{ij}(x)D_ jU]-k(x)U+K(x)U^ p=0\quad in\quad {\mathbb{R}}^ n,$ where $$n\geq 3$$, $$p>1$$ and the functions $$a_{ij}=a_{ji}$$ for $$i,j=1,2,...,n$$ are measurable and satisfy the uniform ellipticity condition. Under some conditions, the author obtains existence and nonexistence results of (1). Moreover, the author also treats a limiting case when K(x) is negative and has quadratic decay at infinity.
Reviewer: Chuanfang Wang

##### MSC:
 35J15 Second-order elliptic equations 35B05 Oscillation, zeros of solutions, mean value theorems, etc. in context of PDEs 35J60 Nonlinear elliptic equations 35B40 Asymptotic behavior of solutions to PDEs
Full Text: