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.
“…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.…”
By using the classical fixed point theorem for operators on cone, in this article, some results of one and two positive solutions to a class of nonlinear first-order periodic boundary value problems of impulsive dynamic equations on time scales are obtained. Two examples are given to illustrate the main results in this article. Mathematics Subject Classification: 39A10; 34B15.
“…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.…”
By using the classical fixed point theorem for operators on cone, in this article, some results of one and two positive solutions to a class of nonlinear first-order periodic boundary value problems of impulsive dynamic equations on time scales are obtained. Two examples are given to illustrate the main results in this article. Mathematics Subject Classification: 39A10; 34B15.
“…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].…”
In this paper, we first introduce a concept of the mean-value of uniformly almost periodic functions on time scales and give some of its basic properties. Then, we propose a concept of pseudo almost periodic functions on time scales and study some basic properties of pseudo almost periodic functions on time scales. Finally, we establish some results about the existence of pseudo almost periodic solutions to dynamic equations 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.…”
In this article, we investigate the multiplicity of positive solutions for a fourth-order system of integral boundary value problem on time scales. The existence of multiple positive solutions for the system is obtained by using the fixed point theorem of cone expansion and compression type due to Krasnosel'skill. To demonstrate the applications of our results, an example is also given in the article.
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