A Liapunov functional for a singular integral equation |
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Authors: | TA Burton |
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Institution: | Northwest Research Institute, 732 Caroline St., Port Angeles, WA, USA |
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Abstract: | We consider a scalar integral equation where a∈L20,∞), while C(t,s) has a significant singularity, but is convex when t−s>0. We construct a Liapunov functional and show that g(t,x(t))−a(t)∈L20,∞) and that x(t)−a(t)→0 pointwise as t→∞. Small perturbations are also added to the kernel. In addition, we consider both infinite and finite delay problems. This paper offers a first step toward treating discontinuous kernels with Liapunov functionals. |
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Keywords: | primary 45D05 45M10 |
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