Nontrivial application of Nielsen theory to differential systems

[摘要] In reply to a problem of Jean Leray concerning application of the Nielsen theory to differential systems for obtaining multiplicity results, we present a nontrivial example of such an application. The emphasis is on the parameter space in order to ensure that no subdomain becomes subinvariant under the related Hammerstein solution operator. To achieve this goal, we develop a general method applicable also for ordinary differential equations with or without uniqueness as well as for upper-Caratheodory differential inclusions. We are not aware that any alternative approach can be employed, even in the single-valued case. (c) 2006 Elsevier Inc. All rights reserved.

[发布日期] 2006-12-01

[关键词] Nielsen number;lower estimate of solutions;nontrivial example;three periodic solutions;no subdomain subinvariantness;differential equations and inclusions