Yarur, Cecilia S. Nonexistence of positive singular solutions for a class of semilinear elliptic systems. (English) Zbl 0853.35038 Electron. J. Differ. Equ. 1996, No. 08, 22 p. (1996). 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. Cited in 6 Documents 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 PDF BibTeX XML Full Text: EuDML EMIS OpenURL