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Entire positive solutions for inhomogeneous semilinear elliptic systems. (English) Zbl 1073.35086

The main goal of this paper is to study the existence and nonexistence problems for inhomogeneous semilinear elliptic systems \[ -\Delta u= v^p+ f(x),\quad x\in \mathbb{R}^n,\qquad -\Delta v= u^q+ g(x),\quad x\in\mathbb{R}^n,\qquad u(x)> 0,\;v(x)> 0,\quad x\in\mathbb{R}^n. \] A criteria of existence and nonexistence of positive solutions is given by the exponents of the rate of nonlinear terms of infinity.

MSC:

35J60 Nonlinear elliptic equations
35J45 Systems of elliptic equations, general (MSC2000)
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