Eigenvalue comparisons for differential equations on a measure chain
Electronic journal of differential equations, Tome 1998 (1998)
The theory of $u_{0}$-positive operators with respect to a cone in a Banach space is applied to eigenvalue problems associated with the second order $\Delta$-differential equation (often referred to as a differential equation on a measure chain) given by $y^{\Delta\Delta}(t)+\lambda p(t)y(\sigma(t))=0, t\in[0,1]$, satisfying the boundary conditions $y(0)=0=y(\sigma^2(1))$. The existence of a smallest positive eigenvalue is proven and then a theorem is established comparing the smallest positive eigenvalues for two problems of this type.
@article{EJDE_1998__1998__a7,
author = {Chyan, Chuan Jen and Davis, John M. and Henderson, Johnny and Yin, William K.C.},
title = {Eigenvalue comparisons for differential equations on a measure chain},
journal = {Electronic journal of differential equations},
year = {1998},
volume = {1998},
zbl = {0912.34067},
language = {en},
url = {http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a7/}
}
TY - JOUR AU - Chyan, Chuan Jen AU - Davis, John M. AU - Henderson, Johnny AU - Yin, William K.C. TI - Eigenvalue comparisons for differential equations on a measure chain JO - Electronic journal of differential equations PY - 1998 VL - 1998 UR - http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a7/ LA - en ID - EJDE_1998__1998__a7 ER -
%0 Journal Article %A Chyan, Chuan Jen %A Davis, John M. %A Henderson, Johnny %A Yin, William K.C. %T Eigenvalue comparisons for differential equations on a measure chain %J Electronic journal of differential equations %D 1998 %V 1998 %U http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a7/ %G en %F EJDE_1998__1998__a7
Chyan, Chuan Jen; Davis, John M.; Henderson, Johnny; Yin, William K.C. Eigenvalue comparisons for differential equations on a measure chain. Electronic journal of differential equations, Tome 1998 (1998). http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a7/