Solvability of boundary value problems with Riemann-Stieltjes Δ-integral conditions for second-order dynamic equations on time scales at resonance

Abstract

In this paper, by making use of the coincidence degree theory of Mawhin, the existence of the nontrivial solution for the boundary value problem with RiemannStieltjes Δ-integral conditions on time scales at resonanceis established, where g(s) = 1. An example is given to illustrate the main results.

Boundary Value Problems for Fourth Order Nonlinearp-Laplacian Difference Equations

“…Before we apply the critical point theory, we will establish the corresponding variational framework for (1) with (2). Let…”

“…In the last decade, by using various techniques such as critical point theory, fix point theory, topological degree theory, and coincidence degree theory, a great deal of works have been done on the existence of solutions to boundary value problems of difference equations (see [1][2][3][4][5][6][7] and references therein). Among these approaches, the critical point theory seems to be a powerful tool to deal with this problem (see [5,[7][8][9]).…”

“…Then, for ∈(1,2],0 = * ( + 1) −(2− )/2 8 /2 (sin 2( + 2) sin 2( + 1) ) , 0 = * ( + 2) (2− )/2 8 /2 (sin (…”

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.…”