existence of singular solutions for a dirichlet problem containing a dirac mass

{−δu = f (x, u, v) + cδ0,

−δv = g(x, u, v) + dδ0 in d′(b),

u = v = 0 on∂b,

where b is the unit ball centered at zero in rⁿ , n ≥ 3, δ₀ is the dirac mass at 0 and c, d are nonnegative constants. no assumptions on the sign of the functions f and g are required. we also characterize the set of (c, d) such that problem (p) admits a solution in some particular cases of the nonlinearities f and g.