## 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)

### Keywords:

nonexistence; subsolutions; biharmonic equations
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