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Asymptotics of the solution to a singularly perturbed integral equation. (English) Zbl 0718.45006
Summary: The leading term of the asymptotics as \(\epsilon \to +0\) of the solution to the equation \(\epsilon h_{\epsilon}+\int^{1}_{-1}\exp (-a| x-y|)h_{\epsilon}(y)dy=f(x),\) \(-1\leq x\leq 1,\) \(f\in C^ 4(-1,1)\) is calculated.

MSC:
45M05 Asymptotics of solutions to integral equations
45B05 Fredholm integral equations
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[1] Ramm, A.G., Numerical solution of integral equations in a space of distributions, J. math. anal. appl., 110, 384-390, (1985) · Zbl 0627.65141
[2] Ramm, A.G., Random fields estimation theory, (1990), Longman Scientific and Wiley New York · Zbl 0712.47042
[3] Ramm, A.G., Theory and applications of some new classes of integral equations, (1980), Springer-Verlag New York · Zbl 0456.45001
[4] A.G. Ramm, Numerical solution of some integral equations in distributions, Computers and Math. with Applications (to appear). · Zbl 0627.65141
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