## Existence and uniqueness of solutions for a semilinear elliptic system.(English)Zbl 1159.35344

Summary: We consider the existence, the nonexistence, and the uniqueness of solutions of some special systems of nonlinear elliptic equations with boundary conditions. In a particular case, the system reduces to the homogeneous Dirichlet problem for the biharmonic equation $$\Delta^2 u = |u|^p$$ in a ball with $$p > 0$$.

### MSC:

 35J60 Nonlinear elliptic equations 35B35 Stability in context of PDEs 35J40 Boundary value problems for higher-order elliptic equations 35J55 Systems of elliptic equations, boundary value problems (MSC2000)
Full Text: