Numerical computations for singular semilinear elliptic boundary value problems

The paper studies a class of Dirichlet problems with homogeneous boundary conditions for singular semilinear elliptic equations in a bounded smooth domain in . A numerical method is devised to construct an approximate Greenʹs function by using radial basis functions and the method of fundamental solutions. An estimate of the error involved is also given. A weak solution of the above given problem is a solution of its corresponding nonlinear integral equation. A computational method is given to find the minimal weak solution U, and the critical index λ* (such that a weak solution U exists for λ < λ*, and U does not exist for λ > λ*).