#### N. Sreedhar, V.V.R.R.B. Raju, Y. Narasimhulu, Existence of positive solutions for higher order boundary value problems with integral boundary conditions on time scales, Vol. 2017 (2017), Article ID 5, pp. 1-13

Full Text: PDF

DOI: 10.23952/jnfa.2017.5

Received September 13, 2016; Accepted November 20, 2016

Abstract. In this paper, we establish the existence of even number of positive solutions for  higher order integral boundary value problems on time scales $(-1)^n u^{{\Delta}^{2n}}(t)=f(t, u),$ $t\in (0, 1)_T,$ $u^{{\Delta}^{2i}}(0)=u^{{\Delta}^{2i}}(1)=\int_{0}^{1}a_{i+1}(x) u^{{\Delta}^{2i}} (x) \Delta x,$ for $0\leq i\leq n-1,$ where $n\geq 1$, by applying the Avery–Henderson fixed point theorem.