# solutions of nonlinear differential equations existence results via the variational approach trends in abstract and applied analysis

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## Solutions Of Nonlinear Differential Equations

**Author :**Lin Li

**ISBN :**9789813108622

**Genre :**Mathematics

**File Size :**84. 43 MB

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Variational methods are very powerful techniques in nonlinear analysis and are extensively used in many disciplines of pure and applied mathematics (including ordinary and partial differential equations, mathematical physics, gauge theory, and geometrical analysis). In our first chapter, we gather the basic notions and fundamental theorems that will be applied throughout the chapters. While many of these items are easily available in the literature, we gather them here both for the convenience of the reader and for the purpose of making this volume somewhat self-contained. Subsequent chapters deal with how variational methods can be used in fourth-order problems, Kirchhoff problems, nonlinear field problems, gradient systems, and variable exponent problems. A very extensive bibliography is also included. Contents:PrefaceSome Notations and ConventionsPreliminaries and Variational PrinciplesQuasilinear Fourth-Order ProblemsKirchhoff ProblemsNonlinear Field ProblemsGradient SystemsVariable Exponent Problems Readership: Graduate students and researchers interested in variational methods.

## Ordinary Differential Equations And Boundary Value Problems

**Author :**John R Graef

**ISBN :**9789813236479

**Genre :**

**File Size :**76. 78 MB

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The authors give a treatment of the theory of ordinary differential equations (ODEs) that is excellent for a first course at the graduate level as well as for individual study. The reader will find it to be a captivating introduction with a number of non-routine exercises dispersed throughout the book. The authors begin with a study of initial value problems for systems of differential equations including the Picard and Peano existence theorems. The continuability of solutions, their continuous dependence on initial conditions, and their continuous dependence with respect to parameters are presented in detail. This is followed by a discussion of the differentiability of solutions with respect to initial conditions and with respect to parameters. Comparison results and differential inequalities are included as well. Linear systems of differential equations are treated in detail as is appropriate for a study of ODEs at this level. Just the right amount of basic properties of matrices are introduced to facilitate the observation of matrix systems and especially those with constant coefficients. Floquet theory for linear periodic systems is presented and used to analyze nonhomogeneous linear systems. Stability theory of first order and vector linear systems are considered. The relationships between stability of solutions, uniform stability, asymptotic stability, uniformly asymptotic stability, and strong stability are examined and illustrated with examples as is the stability of vector linear systems. The book concludes with a chapter on perturbed systems of ODEs. Contents: Systems of Differential EquationsContinuation of Solutions and Maximal Intervals of ExistenceSmooth Dependence on Initial Conditions and Smooth Dependence on a ParameterSome Comparison Theorems and Differential InequalitiesLinear Systems of Differential EquationsPeriodic Linear Systems and Floquet TheoryStability TheoryPerturbed Systems and More on Existence of Periodic Solutions Readership: Graduate students and researchers interested in ordinary differential equations. Keywords: Differential Equations;Linear Systems;Comparison Theorems;Differential Inequalities;Periodic Systems;Floquet Theory;Stability Theory;Perturbed Equations;Periodic SolutionsReview: Key Features: Clarity of presentationTreatment of linear and nonlinear problemsIntroduction to stability theoryNonroutine exercises to expand insight into more difficult conceptsExamples provided with thorough explanations

## Higher Order Boundary Value Problems On Unbounded Domains Types Of Solutions Functional Problems And Applications

**Author :**Minhos Feliz Manuel

**ISBN :**9789813220072

**Genre :**Mathematics

**File Size :**23. 25 MB

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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 (Sturmâ€“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. Contents: Boundary Value Problems on the Half-Line: Third-Order Boundary Value ProblemsGeneral nth-Order ProblemsImpulsive Problems on the Half-Line with Infinite Impulse MomentsHomoclinic Solutions and Lidstone Problems: Homoclinic Solutions for Second-Order ProblemsHomoclinic Solutions to Fourth-Order ProblemsLidstone Boundary Value ProblemsHeteroclinic Solutions and Hammerstein Equations: Heteroclinic Solutions for Semi-Linear Problems (i)Heteroclinic Solutions for Semi-Linear Problems (ii)Heteroclinic Solutions for Semi-Linear Problems (iii)Hammerstein Integral Equations with Sign-Changing KernelsFunctional Boundary Value Problems: Second-Order Functional ProblemsThird-Order Functional ProblemsÏ•-Laplacian Equations with Functional Boundary Conditions Readership: Graduate students and researchers interested in nonlinear analysis. Keywords: Boundary Value Problems in Unbounded Domains;Impulsive Problems with Infinite Impulses;Homoclinic Solutions;Lidstone Problems on the Real Line;Heteroclinic Solutions for Hammerstein Equations;Functional ProblemsReview: Key Features: Presents higher order boundary value and impulsive problems on unbounded domainsElucidates homoclinic and heteroclinic solutions without growth, sign or periodicity assumptions on the nonlinearity, and their relation with Lidstone problems and Hammerstein equations on the real lineExplains clearly the semi-linear and higher order functional problems where the boundary conditions can include nonlocal data and global variation on the unknown functions, such as multi-point, integral, maximum and/or minimum arguments

## Ordinary Differential Equations And Boundary Value Problems Volume Ii Boundary Value Problems

**Author :**Graef John R

**ISBN :**9789813274044

**Genre :**Mathematics

**File Size :**51. 51 MB

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The authors give a systematic introduction to boundary value problems (BVPs) for ordinary differential equations. The book is a graduate level text and good to use for individual study. With the relaxed style of writing, the reader will find it to be an enticing invitation to join this important area of mathematical research. Starting with the basics of boundary value problems for ordinary differential equations, linear equations and the construction of Green's functions are presented clearly.A discussion of the important question of the existence of solutions to both linear and nonlinear problems plays a central role in this volume and this includes solution matching and the comparison of eigenvalues.The important and very active research area on existence and multiplicity of positive solutions is treated in detail. The last chapter is devoted to nodal solutions for BVPs with separated boundary conditions as well as for non-local problems.While this Volume II complements , it can be used as a stand-alone work.

## The Strong Nonlinear Limit Point Limit Circle Problem

**Author :**Graef John R

**ISBN :**9789813226395

**Genre :**Mathematics

**File Size :**21. 20 MB

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The limit-point/limit-circle problem had its beginnings more than 100 years ago with the publication of Hermann Weyl's classic paper in Mathematische Annalen in 1910 on linear differential equations. This concept was extended to second-order nonlinear equations in the late 1970's and later, to higher order nonlinear equations. This monograph traces the development of what is known as the strong nonlinear limit-point and limit-circle properties of solutions. In addition to bringing together all such results into one place, some new directions that the study has taken as well as some open problems for future research are indicated. Contents: The Origins of the Limit-Point/Limit-Circle ProblemEquations with p-LaplacianStrong Limit-Point/Limit-Circle PropertiesDamped EquationsHigher Order EquationsDelay Equations IDelay Equations IITransformations of the Basic EquationNotes, Open Problems, and Future Directions Readership: Graduate students and researchers of mathematics integrated in limit-point/limit circle topics. Keywords: Limit-Point Problem;Limit-Circle Problem;Strong Limit-Point Problem;Strong Limit-Circle Problem;Asymptotic Properties of Solutions;Nonlinear Differential Equations;Second Order Equations;Higher Order EquationsReview: Key Features: There is no other source of results on this problem except for the individual papers that appear in the literature. This work collects all that is known about this problem in one placeThe references on the nonlinear problem are complete up to 2017Directions for future research are indicated

## Solutions Of Nonlinear Differential Equations

**Author :**Lin Li

**ISBN :**9813108606

**Genre :**Differential equations, Nonlinear

**File Size :**76. 68 MB

**Format :**PDF, Mobi

**Download :**322

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Variational methods are very powerful techniques in nonlinear analysis and are extensively used in many disciplines of pure and applied mathematics (including ordinary and partial differential equations, mathematical physics, gauge theory, and geometrical analysis). In our first chapter, we gather the basic notions and fundamental theorems that will be applied throughout the chapters. While many of these items are easily available in the literature, we gather them here both for the convenience of the reader and for the purpose of making this volume somewhat self-contained. Subsequent chapters deal with how variational methods can be used in fourth-order problems, Kirchhoff problems, nonlinear field problems, gradient systems, and variable exponent problems. A very extensive bibliography is also included.

## Differential And Difference Equations With Applications

**Author :**Sandra Pinelas

**ISBN :**9783319756479

**Genre :**Mathematics

**File Size :**81. 91 MB

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This book gathers papers from the International Conference on Differential & Difference Equations and Applications 2017 (ICDDEA 2017), held in Lisbon, Portugal on June 5-9, 2017. The editors have compiled the strongest research presented at the conference, providing readers with valuable insights into new trends in the field, as well as applications and high-level survey results. The goal of the ICDDEA was to promote fruitful collaborations between researchers in the fields of differential and difference equations. All areas of differential and difference equations are represented, with a special emphasis on applications.

## Mathematical Reviews

**Author :**

**ISBN :**UOM:39015078588608

**Genre :**Mathematics

**File Size :**38. 29 MB

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## International Aerospace Abstracts

**Author :**

**ISBN :**UOM:39015057265749

**Genre :**Aeronautics

**File Size :**67. 18 MB

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## Mathematics Of Complexity And Dynamical Systems

**Author :**Robert A. Meyers

**ISBN :**9781461418054

**Genre :**Mathematics

**File Size :**21. 71 MB

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Mathematics of Complexity and Dynamical Systems is an authoritative reference to the basic tools and concepts of complexity, systems theory, and dynamical systems from the perspective of pure and applied mathematics. Complex systems are systems that comprise many interacting parts with the ability to generate a new quality of collective behavior through self-organization, e.g. the spontaneous formation of temporal, spatial or functional structures. These systems are often characterized by extreme sensitivity to initial conditions as well as emergent behavior that are not readily predictable or even completely deterministic. The more than 100 entries in this wide-ranging, single source work provide a comprehensive explication of the theory and applications of mathematical complexity, covering ergodic theory, fractals and multifractals, dynamical systems, perturbation theory, solitons, systems and control theory, and related topics. Mathematics of Complexity and Dynamical Systems is an essential reference for all those interested in mathematical complexity, from undergraduate and graduate students up through professional researchers.