High Order Boundary Value Problems de Joao Fialho

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

Joao Fialho

Feliz Minhós

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.

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Recenzii

"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." - Reviewed by Gennaro Infante, Ph.D., Associate Professor, Department of Mathematics and Computer Science, University of Calabria, Italy

Cuprins

Preface; Introduction; High Order Periodic Problems; New Trends on Lidstone Problems; Multiplicity of Solutions; High Order Periodic Impulsive Problems; High Order Problems with Functional Boundary Conditions; Generalized Ø-Laplacian Equation with Functional Boundary Conditions; Functional Boundary Value Problems; Index.