Abstract and Applied Analysis
Volume 5 (2000), Issue 2, Pages 91-99
doi:10.1155/S108533750000018X

Solvability of a nonlinear second order conjugate eigenvalue problem on a time scale

John M. Davis,1 Johnny Henderson,2 K. Rajendra Prasad,3 and William Yin4

1Department of Mathematics, Baylor University, Waco, TX 76798, USA
2Department of Mathematics, Auburn University, Auburn, AL 36849, USA
3Department of Applied Mathematics, Andhra University, Visakhapatnam 530003, India
4Department of Mathematics, LaGrange College, LaGrange, GA 30240, USA

Received 2 February 2000

Copyright © 2000 John M. Davis et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

We consider the nonlinear second order conjugate eigenvalue problem on a time scale: y ΔΔ(t)+λa(t)f(y(σ(t)))=0,t∈[0,1],y(0)=0=y(σ(1)) . Values of the parameter λ (eigenvalues) are determined for which this problem has a positive solution. The methods used here extend recent results by allowing for a broader class of functions for a(t).