Existence Theory for the Radially Symmetric Contact Lens Equation

In this paper we present a variational formulation of the problem of determining the elastic stresses in a contact lens on an eye and the induced suction pressure distribution in the tear film between the eye and the lens. This complements the force-balance derivation that we used in earlier work [K. L. Maki and D. S. Ross, J. Bio. Sys., 22 (2014), pp. 235--248]. We investigate the existence of solutions of the relevant boundary value problem for the singular, second-order Euler--Lagrange equation. We prove that, for lenses of constant thickness, solutions exist. We present an example to show that in some cases in which the lens thickness increases with distance from the lens center no solution exists.