Multiple positive solutions for first-order impulsive integral boundary value problems on time scales

Abstract

In this paper, we first present a class of first-order nonlinear impulsive integral boundary value problems on time scales. Then, using the well-known GuoKrasnoselskii fixed point theorem and Legget-Williams fixed point theorem, some criteria for the existence of at least one, two, and three positive solutions are established for the problem under consideration, respectively. Finally, examples are presented to illustrate the main results. MSC: 34B10; 34B37; 34N05.

Periodic boundary value problems for nonlinear first-order impulsive dynamic equations on time scales

“…On the other hand, recently, the theory of dynamic equations on time scales has become a new important branch (see, for example, [19][20][21]). Naturally, some authors have focused their attention on the boundary value problems of impulsive dynamic equations on time scales [22][23][24][25][26][27][28][29][30][31][32][33][34][35][36]. However, to the best of our knowledge, few papers concerning PBVPs of impulsive dynamic equations on time scales with semi-position condition.…”

Pseudo almost periodic functions and pseudo almost periodic solutions to dynamic equations on time scales

“…Many papers have been published on the theory of dynamic equations on time scales [1][2][3][4][5][6][7][8][9][10][11][12][13][14]. In addition, the existence of almost periodic, asymptotically almost periodic, pseudo-almost periodic solutions is among the most attractive topics in the qualitative theory of differential equations and difference equations due to their applications, especially in biology, economics and physics [15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33][34].…”

Multiple positive solutions for a fourth-order integral boundary value problem on time scales

“…However, the corresponding results for BVP with integral boundary conditions on time scales are still very few [19][20][21]. In this article, we discuss the multiple positive solutions for the following fourth-order system of integral BVP with a parameter on time scales (4 ) (t) + λf (t, x(t), x (t), x (t), y(t), y (t), y (t)) = 0, t ∈ (0, σ (T)) T , y (4 ) The main purpose of this article is to establish some sufficient conditions for the existence of at least two positive solutions for system (1.1) by using the fixed point theorem of cone expansion and compression type.…”