Iteration Procedures of Shuttle Iteration Type in Continuous Non-Monotone Problems

D. Rachinskii
2001 Zeitschrift für Analysis und ihre Anwendungen  
We suggest and study iteration procedures converging from below and above to robust stable solutions and to robust stable continuous branches of solutions for quasilinear boundary-value problems with continuous non-monotone non-linearities. The iterations are constructed by modifications of the shuttle iteration method, which is used in problems with monotone operators leaving invariant a cone interval. 1) The general theory of Banach spaces with cone semiordering can be found in [4, 11] . We
more » ... ly use some notation and simple facts. 2) This set is called a cone interval. 3) We consider perturbations of the non-linearity only. Also, it is possible to consider perturbations both of the linear and nonlinear parts of the problem.
doi:10.4171/zaa/1058 fatcat:3vl33nuqavazxjft7lixoonupq