Asymptotic behaviour at infinity of solutions of multidimensional second kind integral equations (Q1908807)

This is the continuation of the two earlier works of the first author [ibid. 4, No. 2, 153-177 (1992; Zbl 0756.45004)]. Let \(\Omega \subset \mathbb{R}^n\) be an unbounded open set and let \(X\) be the space of bounded and continuous functions on \(\overline \Omega\). For \(p \geq 0\), let \(W_p (s) = (1 + |s |)^p\) and let \(X_p\) denote the weighted space \(X_p : = \{x \in X : |x |^p_\infty : = |w_p x |_\infty < \infty\}\). In the space \(X_p\), the integral equation \[ x(s) - \int_\Omega k (s,t) x(t)dt = y(s),\;s \in \overline \Omega \] is considered. An application to acoustics is given.