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

Dalmasso, Robert

Int. J. Math. Math. Sci. 2005, No. 10, 1507-1523 (2005).

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)