Twin solutions of boundary value problems for ordinary differential equations and finite difference equations

Periodic boundary value problems for fırst order dynamic equations on time scales

“…Especially, the study of impulsive dynamic equations on time scales has also attracted much attention since it provides an unifying structure for differential equations in the continuous cases and the finite difference equations in the discrete cases, see [5][6][7][8][9][10][11][12][13][14][15][16][17] and references therein. Most of them were devoted to the existence of solutions for periodic boundary value problems (PBVP) by means of some fixed point theorems [18][19][20][21][22] such as the Tarski's fixed point theorem [17], Guo-Krasnoselskii fixed-point theorem [18], and twin fixed-point theorem in a cone [19], etc.. Li et al [4] considered the following periodic boundary value problem with impulses ⎧ ⎨ ⎩ u (t) = g(t, u(t), u(θ (t))), t ∈ J = [0, T], t = t k , u(t k ) = I k (u(t k )), k = 1, 2, ..., p, u(0) = u(T), (1:1) where 0 = t 0 <t 1 <t 2 < ... <t p <t p+1 = T, J 0 = J\{t 1 , ..., t p }, g C(J × R 2 , R), and θ C(J, R), 0 ≤ θ(t) ≤ t, t J, u(t k ) = u(t + k ) − u(t k ). In [6], the authors discussed the following periodic boundary value problem by using the upper and lower solution method and monotone iterative technique …”

Monotone and convex positive solutions for fourth-order multi-point boundary value problems

“…Owing to its importance in application, the existence of positive solutions for nonlinear second and higher order boundary value problems has been studied by many authors. We refer to recent contributions of Ma [1][2][3], He and Ge [4], Guo and Ge [5], Avery et al [6,7], Henderson [8], Eloe and Henderson [9], Yang et al [10], Webb and Infante [11,12], and Agarwal and O'Regan [13]. For survey of known results and additional references, we refer the reader to the monographs by Agarwal [14] and Agarwal et al [15].…”

Positive solutions of boundary value problem for singular positone and semi-positone third-order difference equations

“…We refer the reader to [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] and references therein. In [16], the authors studied the following boundary value problem:…”