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Nonexistence of positive singular solutions for a class of semilinear elliptic systems. (English) Zbl 0853.35038

Summary: We study nonexistence and removability results for nonnegative subsolutions to \[ \Delta u= a(x) v^p,\quad \Delta v= b(x) u^q\quad \text{in } \Omega\subset \mathbb{R}^n,\quad N\geq 3, \] where \(p\geq 1\), \(q\geq 1\), \(pq> 1\), and \(a\) and \(b\) are nonnegative functions. As a consequence of this work, we obtain new results for biharmonic equations.

MSC:

35J60 Nonlinear elliptic equations
31A30 Biharmonic, polyharmonic functions and equations, Poisson’s equation in two dimensions
35J20 Variational methods for second-order elliptic equations
35J45 Systems of elliptic equations, general (MSC2000)
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