%0 Journal Article
%T Structure of Eigenvalues of Multi-Point Boundary Value Problems
%A Jie Gao
%A Dongmei Sun
%A Meirong Zhang
%J Advances in Difference Equations
%D 2010
%I Springer
%R 10.1155/2010/381932
%X The structure of eigenvalues of  y¡å+q(x)y=¦Ëy, y(0)=0, and y(1)=¡Æk=1m¦Áky(¦Çk), will be studied, where q¡ÊL1([0,1], ), ¦Á=(¦Ák)¡Ê m, and 0<¦Ç1< <¦Çm<1. Due to the nonsymmetry of the problem, this equation may admit complex eigenvalues. In this paper, a complete structure of all complex eigenvalues of this equation will be obtained. In particular, it is proved that this equation has always a sequence of real eigenvalues tending to +¡Þ. Moreover, there exists some constant Aq>0 depending on q, such that when ¦Á satisfies ¡¬¦Á¡¬¡ÜAq, all eigenvalues of this equation are necessarily real.
%U http://dx.doi.org/10.1155/2010/381932