| Abstract: |
| Positone and semipositone problems have been of great interest to the PDE community for many years now due to the frequency with which they appear in reaction-diffusion models and the theory of nonlinear heat generation. While these problems pose many interesting theoretical challenges, they also pose particular challenges when attempt to find numerical approximations to solutions. We discuss recent results showing that a simple finite difference method, which adapts techniques from the method of sub- and supersolutions, can not only find approximate solutions, but also detects multiplicity and nonuniqueness for a wide class of sublinear problems in one or more dimensions. |
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