Boundary-value problems for shallow elastic membrane caps
Panos K. Palamides · IMA Journal of Applied Mathematics · 2002
Consider the general nonlinear boundary‐value problem (p(t) y′ (t))′ = p(t)q(t) f (t, y(t), y′ (t)), t ≥ 1, g(y(1), y′ (1)) = 0, where the function f may be singular at the point y(1) = 0 and p(1) ≥ 0. We obtain conditions which guarantee existence of positive and bounded solutions of the above problem. As an application we prove existence and uniqueness of rotationally symmetric solutions to a nonlinear boundary‐value problem, representing the elastic deformation of a spherical cap.