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Nonlinear Higher Order Differential And Integral Coupled Systems: Impulsive And Integral Equations On Bounded And Unbounded... Nonlinear Higher Order Differential And Integral Coupled Systems: Impulsive And Integral Equations On Bounded And Unbounded Domains (Hardcover)
Feliz Manuel Minhos, Robert De Sousa
R2,488 Discovery Miles 24 880 Ships in 10 - 15 working days

Boundary value problems on bounded or unbounded intervals, involving two or more coupled systems of nonlinear differential and integral equations with full nonlinearities, are scarce in the literature. The present work by the authors desires to fill this gap. The systems covered here include differential and integral equations of Hammerstein-type with boundary constraints, on bounded or unbounded intervals. These are presented in several forms and conditions (three points, mixed, with functional dependence, homoclinic and heteroclinic, amongst others). This would be the first time that differential and integral coupled systems are studied systematically. The existence, and in some cases, the localization of the solutions are carried out in Banach space, following several types of arguments and approaches such as Schauder's fixed-point theorem or Guo-Krasnosel'ski? fixed-point theorem in cones, allied to Green's function or its estimates, lower and upper solutions, convenient truncatures, the Nagumo condition presented in different forms, the concept of equiconvergence, Caratheodory functions, and sequences. Moreover, the final part in the volume features some techniques on how to relate differential coupled systems to integral ones, which require less regularity. Parallel to the theoretical explanation of this work, there is a range of practical examples and applications involving real phenomena, focusing on physics, mechanics, biology, forestry, and dynamical systems, which researchers and students will find useful.

Nonlinear Differential Equations and Dynamical Systems - Theory and Applications (Hardcover): Feliz Manuel Minhos, Joao Fialho Nonlinear Differential Equations and Dynamical Systems - Theory and Applications (Hardcover)
Feliz Manuel Minhos, Joao Fialho
R1,083 Discovery Miles 10 830 Ships in 12 - 17 working days
Higher Order Boundary Value Problems On Unbounded Domains: Types Of Solutions, Functional Problems And Applications... Higher Order Boundary Value Problems On Unbounded Domains: Types Of Solutions, Functional Problems And Applications (Hardcover)
Feliz Manuel Minhos, Hugo Alexandre Sacristao Carrasco
R2,371 Discovery Miles 23 710 Ships in 12 - 17 working days

This volume provides a comprehensive overview on different types of higher order boundary value problems defined on the half-line or on the real line (Sturm-Liouville and Lidstone types, impulsive, functional and problems defined by Hammerstein integral equations). It also includes classical and new methods and techniques to deal with the lack of compactness of the related operators.The reader will find a selection of original and recent results in this field, conditions to obtain solutions with particular qualitative properties, such as homoclinic and heteroclinic solutions and its relation with the solutions of Lidstone problems on all the real line.Each chapter contains applications to real phenomena, to classical equations or problems, with a common denominator: they are defined on unbounded intervals and the existing results in the literature are scarce or proven only numerically in discrete cases.The last part features some higher order functional problems, which generalize the classical two-point or multi-point boundary conditions, to more comprehensive data where an overall behavior of the unknown functions and their derivatives is involved.

New Trends in Differential and Difference Equations and Applications (Paperback): Feliz Manuel Minhos, Joao Fialho New Trends in Differential and Difference Equations and Applications (Paperback)
Feliz Manuel Minhos, Joao Fialho
R1,296 R1,090 Discovery Miles 10 900 Save R206 (16%) Ships in 10 - 15 working days
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