On the elliptic equation \(D_ i[a_{ij}(x)D_ jU]-k(x)U+K(x)U^ p=0\). (English) Zbl 0584.35031

Lin, Fang-Hua

Proc. Am. Math. Soc. 95, 219-226 (1985).

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

Keywords:

entire positive solutions; uniform ellipticity condition