We show the existence of at least one weak solution for a threepoint boundary-value problem of Kirchhoff-type. Our technical approach is based on variational methods. In addition, an example to illustrate our results is given.

The acoustic backscatter from pressure release prolate spheroids and a three-dimensional representation of a fish swimbladder (Chilean jack mackerel, Trachurus symmetricus murphyi) was calculated using four target strength models (Kirchhoff-approximation, Kirchhoff-ray-mode, finite element solution of the Helmholtz equation, and prolate-spheroid-modal-series). Smoothly varying errors were found...