High Order Boundary Value Problems: Existence, Localization and Multiplicity Results

João Fialho
College of the Bahamas, Nassau, Bahamas

Feliz Minhós
Universidade de Évora, Évora, Portugal

Series: Mathematics Research Developments
BISAC: MAT000000

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Volume 10

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Special issue: Resilience in breaking the cycle of children’s environmental health disparities
Edited by I Leslie Rubin, Robert J Geller, Abby Mutic, Benjamin A Gitterman, Nathan Mutic, Wayne Garfinkel, Claire D Coles, Kurt Martinuzzi, and Joav Merrick

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The motto for all the results presented in this book is the lower and upper solution method. In short, this method can guarantee not only the existence of a solution for a given boundary value problem but also the location of the solution in a strip defined by the lower and the upper solutions. Therefore, the challenge of finding a solution for a boundary value problem is replaced by the search of two functions (well-ordered, in reversed order or non-ordered) satisfying adequate differential inequalities and boundary conditions. The freedom to choose such functions is at the same time its weakness: lower and upper solutions must be defined and exhibited. (Imprint: Novinka )

Preface

Introduction

I - NONLINEAR BOUNDARY VALUE PROBLEMS: EXISTENCE AND MULTIPLICITY RESULTS

Chapter 1. High Order Periodic Problems

Chapter 2. New Trends on Lidstone Problems

Chapter 3. Multiplicity of Solutions

Chapter 4. High Order Periodic Impulsive Problems

II - FUNCTIONAL BOUNDARY VALUE PROBLEMS

Chapter 5. High Order Problems with Functional Boundary Conditions

Chapter 6. Generalized f−Laplacian Equation with Functional Boundary Conditions

Chapter 7. Functional Boundary

References

"This very interesting book is devoted to the study of higher order boundary value problems. The main tool utilized throughout the volume is the method of upper and lower solutions. Of particular interest is the fact that in many cases the authors give an explicit construction of the upper and lower solution. The authors illustrate how this location tool can be utilized to gain qualitative information regarding the solutions: existence, multiplicity, monotonicity. Another nice feature of the book is that the methodology is applied also to real world phenomena: the London Millenium bridge and the periodic oscillations of the axis of a satellite. Overall the book is fairly easy to read and would be helpful for graduate students and young researchers willing to learn more on this method." - Gennaro Infante, Ph.D., Associate Professor, Department of Mathematics and Computer Science, University of Calabria, Italy

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These contents have of wide scope amongst researchers in various areas like Mathematics, Engineering and Finance as they offer applications to theoretical problems as well as techniques to build and define lower and upper solutions for higher order problems. It is also very useful for students from undergraduate to graduate level in those fields as it provides arguments based on elementary and basic concepts, without "deep mathematics tools" and includes examples, where lower and upper solutions are properly defined and applied.

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