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Nonlinear Differential Equations in Ordered Spaces provides the theoretical framework for developing new methods that allow the treatment of a variety of discontinuous initial and boundary value problems for both ordinary and partial differential equations, in explicit and implicit forms. This volume includes research that appears for the first time in book form and is designed as a source book for pure and applied mathematicians. However, the self-contained presentation along with numerous worked examples and complete, detailed proofs make this book accessible to researchers in engineering as well as advanced students in these fields.