First order periodic problem at resonance with nonlinear impulses

Boundary value problems

Martina Langerov¹  Pavel Drbek² 

[1] , Czech Republic;Department of Mathematics, University of West Bohemia, PlzeňNTIS, University of West Bohemia, Plzeň

关键词: impulsive differential equations;    Landesman-Lazer conditions;    topological degree theory;    Schaeffer fixed point theorem;   

DOI  :  10.1186/s13661-014-0186-3

学科分类：数学（综合）

来源: SpringerOpen

【 摘 要 】

We consider the nonlinear first order periodic problem with nonlinear impulses. We apply the Schaeffer fixed point theorem and prove the existence results under Landesman-Lazer type sufficient conditions. We formulate also necessary conditions in some special cases. The impulses can be viewed as a control which compensates the influence of external forces and vice versa. MSC: 34A37, 34B37, 34F15, 47H11.

【 授权许可】

CC BY