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

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).