摘要
利用拓扑度理论研究下列高阶非线性常微分方程{u(n)+a(t)f(t,u)=0,u(i)(0)=0,i=1,2,…,n-2,u(0)=∫01u(τ)dα(τ),u′(1)=∫01u′(τ)dβ(τ).非平凡解的存在性,其中f∈C([0,1]×,),a∈L(0,1),a在[0,1]上可奇异且非负,满足∫01a(t)dt>0.对超线性和次线性都做到了第一特征值,本质推广和改进了现有文献的结果.
This article is concerned with the existence of nontrivial solutions to the higher order boundary value problems by using topological degree theory.{u（n）＋a（t）f（t,u）=0,u（i）（0）=0,i=1,2,…,n-2,u（0）=∫01u（τ）dα（τ）,u′（1）=∫01u′（τ）dβ（τ）.where f∈C（[0,1]×,）,a∈L（0,1）,a is nonnegative and may be singular at[0,1],with ∫10a（t）dt0.Our main results for both the superlinear case and the sublinear case are in terms of the first eigenvalues of associated linear integral operators,essentially extending and improving the existing results in the literature.
出处
《青岛理工大学学报》
CAS
2011年第2期106-112,共7页
Journal of Qingdao University of Technology
关键词
非平凡解
奇异边值问题
锥
谱半径
拓扑度
nontrivial solution
singular boundary value problem
cone
spectral radius
