occurs in the theory of small transverse deflections of stretched thin elastic plates. Here U(X, y) is the deflection of the midplane of the plate, Au = u,, + uyy , and differentiation is indicated by subscripts. In the situation of interest, X is assumed large; it depends on the tension in the plate, the plate thickness, and certain material constants. A second example concerns the system of differential equations for the stress function ~(x, y) and the transverse deflection ru(x, y) of the shallow hyperbolic paraboloidal shell. This system can be reduced to the form