Differential equations and elliptic inequalitties

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My NSERC-supported research contributes to the study of some modeling ordinary differential equations and some second order elliptic inequalities. These modeling equations arise from mechanics, biomechanics and fluid dynamics. For example, they include singular second order ordinary differential equations describing the large deflection membrane response of a spherical cap; higher order ordinary differential equations describing the lateral bending of human spine under muscle forces and other transverse loads; the Falkner-Skan equation arising in boundary layer theory and describing the steady two-dimensional flow of a slightly viscous incompressible fluid past wedge shaped bodies. A new theory of variational inequalities will be established in order to give a partial answer to an open question in the field of partial differential inequalities.