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.


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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