... right-continuous, and thus, is continuous.By (11) and (14), we have ηk ≤ fu(0, x) ≤ k, and so −(1 −η) k ≤ fu(0, x) −k ≤ 0 for every10Figure 1: Infinite beam on nonlinear and non-uniform elastic ... Cq(R) if u ∈ Cq(R) for q = 0, 1, 2, . . (F2) f(u, x) ·u ≥ 0, and fu(u, x) ≥ 0 for every u, x ∈ R.(F3) For every υ ≥ 0, supx∈R, |u|≤υ∂qf∂uq(u, x)< ∞ for q = 0, 1, 2.(F4) ... · ||u||∞ for every u ∈ L∞(R). Thus, K[u] ∈ L∞(R) for every u ∈ L∞(R).(b) For every u ∈ C(R) ∩ L∞(R), we have K[u](i)∞≤ (ταi/k) exp(3iπ/4) ·||u||∞ for i = 1, 2, 3, and K[u](4)∞<...