Drabek P. Solvability and Bifurcations of Nonlinear Equations

Longman Sc & Tech, 1991. — 227 p.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.List of symbolsWeakly nonlinear problems
Problems of Landesman-lazer type
- Dirichlet problem for ordinary differential equations of second order
- Periodic problem for ordinary differential equations of second order
- Dirichlet problem for partial differential equations of higher order with nonlinearity dependent on derivatives
Weakly nonlinear problems with vanishing nonlinearity
- Dirichlet problem for higher order partial differential equations
- Neumann problem for second order partial differential equations
- Dirichlet problem for second order partial differential equations
Weakly nonlinear problems with oscillating nonlinearity
- Neumann problem for second order partial differential equations
- Periodic problem for second order ordinary differential equation
- Periodic problem for system of second order ordinary differential equations
Strongly nonlinear problems
Solvability of strongly nonlinear problems
- Ranges of homogeneous operators
- Fucik's spectrum for strongly nonlinear homogeneous problems
- Perturbation of homogeneous problems - nonresonance case
- Perturbation of homogeneous problems - resonance case
Bifurcations of strongly nonlinear problems
- Global bifurcation results for p-laplacian
- Local bifurcation of generalized spectrumSubject index
Author index