Nonlinear Differential Equations in Ordered Spaces

ISBN: 9781584880684 出版年：2000 页码：330 Carl, S Heikkila, Seppo CRC Press

OPERATOR EQUATIONS IN ORDERED SPACES AND FIRST APPLICATIONS Operator Equations in Ordered Spaces Applications to Differential Equations EXTREMALITY RESULTS FOR FIRST ORDER DIFFERENTIAL EQUATIONS Explicit Initial Value Problems Explicit Boundary Value Problems Explicit Functional Problems Implicit Functional Problems UNIQUENESS, COMPARISON AND WELL-POSEDNESS RESULTS FOR QUASILINEAR DIFFERENTIAL EQUATIONS First Order Boundary Value Problems First Order Initial Value Problems Well-Posedness Results Second Order Problems SECOND ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS Explicit Sturm-Liouville Boundary Value Problems Implicit Sturm-Liouville Boundary Value Problems Convergence of Successive Approximations Explicit Phi-Laplacian Problems Implicit Phi-Laplacian Problems EXTREMALITY RESULTS FOR QUASILINEAR PDE Quasilinear Elliptic Boundary Value Problems Quasilinear Parabolic Problems Discontinuous Quasilinear Problems DIFFERENTIAL INCLUSIONS OF HEMIVARIATIONAL INEQUALITY TYPE Quasilinear Elliptic Inclusions with State-Dependent Subdifferentials State-Dependent Subdifferentials Perturbed by Discontinuous Nonlinearities Elliptic Inclusions with Generalized Gradients Quasilinear Parabolic Inclusions with State-Dependent Subdifferentials DISCONTINUOUS IMPLICIT ELLIPTIC AND PARABOLIC PROBLEMS Statement of the Problem and Notations Preliminaries Main Results Implicit Elliptic Problems APPENDIX Analysis in Ordered Spaces Inequalities Sobolev Spaces Pseudomonotone and Quasilinear Elliptic Operators Nonlinear First Order Evolution Equations Nonsmooth Analysis