Eigenvalue comparisons for differential equations on a measure chain

Chyan, Chuan Jen ; Davis, John M. ; Henderson, Johnny ; Yin, William K.C.

Electronic Journal of Differential Equations, Tome 1998 (1998).

Résumé

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 $\mathrm{\Delta }$-differential equation (often referred to as a differential equation on a measure chain) given by $y^{\mathrm{\Delta }\mathrm{\Delta }}(t)+\lambda p(t)y(\sigma (t))=0,t\in [0,1]$, 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.

Détail

Classification : 34B99, 39A99
Mots-clés : measure chain