Solvability and Bifurcations of Nonlinear Equations

✍ Scribed by Pavel Drabek

• Publisher: Longman Sc & Tech
• Year: 1992
• Tongue: English
• Leaves: 242
• Series: Research Notes in Mathematics Series
• Category: Library

✦ Synopsis

This Research Note describes the state of the investigation of nonlinear boundary value problems for ordinary and partial differential equations. The first part of the book is devoted to the study of weakly nonlinear problems. The author considers Landesman-Lazer type problems for ordinary and partial differntial equations, weakly nonlinear problems with vanishing nonlinearity and weakly nonlinear problems with oscillating nonlinearity. The second part of the book deals with strongly nonlinear problems for ordinary and partial differntial equations. Existence and multiplicity results are proved for both weakly and strongly nonlinear boundary value problems. The strongly nonlinear bifurcation problems are also discussed in this Research Note. The global bifurcation results complete in a certain sense the results of Rabinowitz. The local bifurcation of Fucik's spectrum of strongly nonlinear problems is also investigated. The methods used here are a combination of the results obtained from classical mathematical analysis and recent results derived from nonlinear functional analysis, function spaces and the theory of nonlinear boundary value problems for ordinary and partial differential equations. It is aimed at researchers and graudate students working in analysis, particularly in the theory of nonlinear boundary value problems for differential equations. This book will also be of interest to those working in related fields such as physics and mechanics.

✦ Table of Contents

PREFACE
LIST OF SYMBOLS
INTRODUCTION

PART I
WEAKLY NONLINEAR PROBLEMS
Chapter 1
PROBLEMS OF LANDESMAN-LAZER TYPE
1. Dirichlet problem for ordinary differential equations of second order
2. Periodic problem for ordinary differential equations of second order
3. Dirichlet problem for partial differential equations of higher order with nonlinearity dependent on derivatives
Chapter 2
WEAKLY NONLINEAR PROBLEMS WITH VANISHING NONLINEARITY
4. Dirichlet problem for higher order partial differential equations
5. Neumann problem for second order partial differential equations
6. Dirichlet problem for second order partial differential equations
Chapter 3
WEAKLY NONLINEAR PROBLEMS WITH OSCILLATING NONLINEARITY
7. Neumann problem for second order partial differential equations
8. Periodic problem for second order ordinary differential equation
9. Periodic problem for system of second order ordinary differential equations

PART II
STRONGLY NONLINEAR PROBLEMS
Chapter 4
SOLVABILITY OF STRONGLY NONLINEAR PROBLEMS
10. Ranges of homogeneous operators
11. Fucik's spectrum for strongly nonlinear homogeneous problems
12. Perturbation of homogeneous problems - nonresonance case
13. Perturbation of homogeneous problems - resonance case
Chapter 5
BIFURCATIONS OF STRONGLY NONLINEAR PROBLEMS
14. Global bifurcation results for p-laplacian
15. Local bifurcation of generalized spectrum

REFERENCES
SUBJECT INDEX
AUTHOR INDEX

✦ Subjects

Математика;Дифференциальные уравнения;Обыкновенные дифференциальные уравнения;