Nonlinear Differential Equations in Ordered Spaces
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A01=S. Carl
A01=Seppo Heikkila
advanced mathematics textbook
Author_S. Carl
Author_Seppo Heikkila
boundary
boundary value problems
Caratheodory Function
Category=PBKJ
Category=PBW
Category=PHU
Convex Functionals
dierential
Dierential Equations
discontinuous solutions
elliptic
eq_bestseller
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
eq_non-fiction
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Equation Lu
existence theory for differential equations
extremal
Extremal Solutions
Functional Initial Conditions
Generalized Directional Derivative
greatest
Hemivariational Inequalities
Lebesgue's Dominated Convergence Theorem
Linear Elliptic Boundary
Lower Order Terms
Lower Solutions
mathematical analysis
Monotone Iteration
Monotone Iterative Technique
Natural Partial Ordering
nonlinear operator theory
Order Evolution Equations
Order Interval
Parabolic Problems
partial
Partial Dierential Equations
point
Quasilinear Elliptic Equations
Solution Set
solutions
Special Test Function
theorem
Uniqueness Results
variational methods
xed
Xed Point
Xed Point Theorem
Product details
- ISBN 9781584880684
- Weight: 780g
- Dimensions: 156 x 234mm
- Publication Date: 14 Jun 2000
- Publisher: Taylor & Francis Inc
- Publication City/Country: US
- Product Form: Hardback
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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. By means of these extremality results, the authors prove the existence of extremal solutions between appropriate upper and lower solutions of first and second order discontinuous implicit and explicit ordinary and functional differential equations. They then study the dependence of these extremal solutions on the data.
The authors begin by developing an existence theory for an abstract operator equation in ordered spaces and offer new tools for dealing with different kinds of discontinuous implicit and explicit differential equation problems. They present a unified approach to the existence of extremal solutions of quasilinear elliptic and parabolic problems and extend the upper and lower solution method to elliptic and parabolic inclusion of hemivariation type using variational and nonvariational methods.
Nonlinear Differential Equations in Ordered Spaces includes research that appears for the first time in book form and is designed as a source book for pure and applied mathematicians. Its self-contained presentation along with numerous worked examples and complete, detailed proofs also make it accessible to researchers in engineering as well as advanced students in these fields.
Carl, S.; Heikkila, Seppo
