Geodesic
Eigenvalue comparisons for differential equations on a measure chain
Electronic Journal of Differential Equations, Tome 1998 (1998).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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.
Classification : 34B99, 39A99
Keywords: measure chain 
@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},
     publisher = {mathdoc},
     volume = {1998},
     year = {1998},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_1998__1998__a7/}
}
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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/