Existence of positive solutions for non-positive higher-order BVPs

An application of Schauder’s fixed point theorem with respect to higher order BVPs

“…From the results of Agarwal and Wong [1], [2], [3], we can see that          (E * * ) w (n) (t) + g(t, u(t), w (1) (t), · · · , w (n−2) (t)) = 0 for t ∈ (0, 1) and n ≥ 2, Therefore, our main result generalizes all the recent investigations about the existence of non-negative solutions of (BVP).…”

Positive solutions for a higher-order four-point boundary value problem with a p-Laplacian

“…Motivated by some of such investigations, in [14], Agarwal and Wong studied the following higher-order BVP: (t, u(t), u (t), . .…”

Existence of positive solutions for various boundary value problems

“…, m − 2), 0 < ξ 1 < ξ 2 < · · · < ξ m−2 < 1, m−2 i=1 k i ξ i < 1, and (BC 3 ) u(0) = cu(ξ ), u(1) = bu(η), with 0 < ξ < η < 1, 0 ≤ c ≤ 1 1−ξ , cξ(1 − b) + (1 − c)(1 − bη) > 0 and 0 ≤ b ≤ 1 η . The motivation for the present work stems from many recent investigations in [1][2][3][4][5]. In fact, particular cases of the boundary value problems (BVP j ) occur in various physical phenomena [4,[6][7][8][9][10][11], specially such as gas diffusion through porous media, thermal self-ignition of a chemically active mixture of gases in a vessel [9], catalysis theory [10], chemically reacting systems, as well as adiabatic tubular reactor processes.…”

“…In fact, particular cases of the boundary value problems (BVP j ) occur in various physical phenomena [4,[6][7][8][9][10][11], specially such as gas diffusion through porous media, thermal self-ignition of a chemically active mixture of gases in a vessel [9], catalysis theory [10], chemically reacting systems, as well as adiabatic tubular reactor processes. For the other related works, we refer to recent contributions of Agarwal and Wong [1][2][3], Anuradaha, Hai and Shivaji [6], Bailey, Shampine and Waltman [7], Erbe and Wang [4], Lee and O'Regan [12], Henderson [13], Kelevedjiev [14,15] and Wong, Lian, Lin and Yu [16] and the references therein.…”