Symmetric Positive Solutions for Second Order Boundary Value Problems With Integral Boundary Conditions on Time Scales

Denumerably Many Symmetric Positive Solutions for System of Even Order Singular Boundary Value Problems on Time Scales K. Rajendra Prasad and Mahammad Khuddush

“…In 2010, Hamal and Yoruk [14] established the existence of a symmetric positive solution of the following boundary value problem, q(t)φ p(t)u ∆∇ ∆∇ (t) = λf t, u(t) , t ∈ (0, 1) T , u(0) = u(1) = 1 0 g(s)u(s)∇s, q(0)φ(p(0)u ∆∇ (0)) = q(1)φ(p(1)u ∆∇ (1)) = 1 0 h(s)q(s)φ(p(s)u ∆∇ (s))∇s, (1) by using a fixed point index theory. In 2016, Oguz and Topal [21] considered the following boundary value problem on time scales, u ∆∇ (t) + f t, u(t), u ∆ (t) = 0, t ∈ (a, b) T , αu(a) − β lim…”

“…(t, y)∇t = 1 (t, y)∇t + (t, y)∇t,(23) we use(21) and(22) and the fact that, ifA ∩ B = ∅, then χ[A] • χ[B] = 0 to simplify the integrand, ∞ i=1 χ[z i , z i−1 ] |t − t i | y k , z i−1 ] |t − t k | y χ[z i−k+1 , z i−k ] |t − t i−k+1 | y = ∞ i=1 χ[z i , z i−1 ] |t − t i | 2y a.e.,and so (23) may be written as (t, y)∇t = l , z l−1 ]|t −…”