Stable solutions to semilinear elliptic equations for operators with variable coefficients

Singular Solutions for some Semilinear Elliptic Equations

We are concerned with the behavior of u near x = O. There are two distinct cases: 1) When p >= N / ( N -2) and (N ~ 3) it has been shown by BR~ZIS & V~RON [9] that u must be smooth at 0 (See also BARAS & PIERRE [1] for a different proof). In other words, isolated singularities are removable. 2) When 1-< p < N / ( N 2) there are solutions of (1) with a singularity at x ---0. Moreover all singula...

Oscillation of Semilinear Elliptic Equations with Integrable Coefficients

Some oscillation criteria for the second order semilinear elliptic differential equation

Multiple Nontrivial Solutions of Elliptic Semilinear Equations

We find multiple solutions for semilinear boundary value problems when the corresponding functional exhibits local splitting at zero.

Existence of positive solutions of some semilinear elliptic equations with singular coefficients

Reduced Systems for Three-Dimensional Elliptic Equations with Variable Coefficients

We consider large sparse nonsymmetric linear systems arising from finite difference discretization of three-dimensional (3D) convection-diffusion equations with variable coefficients. We show that performing one step of cyclic reduction yields a system of equations which is well conditioned and for which fast convergence can be obtained. A certain block ordering strategy is applied, and analyti...