Carl S., Heikkila S. Nonlinear Differential Equations in Ordered Spaces

New York: Chapman and Hall/CRC, 2000. — 330 p.Extremality results proved in this Monograph for an abstract operator equation provide 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.Operator Equations in Ordered Spaces and First Applications.
Extremality Results for First Order Differential Equations.
Uniqueness, Comparison and Well-Posedness Results for Quasilinear Differential Equations.
Second Order Functional Differential Equations.
Extremality Results for Quasilinear PDE.
Differential Inclusions of Hemivariational Inequality Type.
Discontinuous Implicit EIlliptic and Parabolic Problems.
Appendix.