Positive solutions to singular multi-point dynamic eigenvalue problems with mixed derivatives Original Research Article

This paper considers a singular mm-point dynamic eigenvalue problem on time scales TT: View the MathML source−(p(t)uΔ(t))∇=λf(t,u(t)),t∈(0,1]∩T, Turn MathJax on View the MathML sourceu(0)=∑i=1m−2aiu(ξi),γu(1)+δp(1)uΔ(1)=∑i=1m−2bip(ξi)uΔ(ξi). Turn MathJax on We allow f(t,w)f(t,w) to be singular at w=0w=0 and t=0t=0. By constructing the Green’s function and studying its positivity, eigenvalue intervals in which there exist positive solutions of the above problem are obtained by making use of the fixed point index theory.