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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