Existence of Weak Solutions for Second-Order Boundary Value Problem of Impulsive Dynamic Equations on Time Scales

Abstract

We study the existence of weak solutions for second-order boundary value problem of impulsive dynamic equations on time scales by employing critical point theory.

Positive Periodic Solutions in Shiftsδ±for a Class of Higher-Dimensional Functional Dynamic Equations with Impulses on Time Scales

“…As is known to all, both continuous and discrete systems are very important in implementation and application. The study of dynamic equations on time scales, which unifies differential, difference, ℎ-difference, and -differences equations and more, has received much attention; see, for example, [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16] and the references therein. The theory of dynamic equations on time scales was introduced by Hilger in his PhD thesis in 1988 [5].…”

Variational approach to second-order impulsive dynamic equations on time scales

“…Sobolev spaces of functions on time scales, which were first introduced in [15] opened a very fruitful new approach in the study of dynamic equations on time scales: the use of variational methods in the context of the boundary value problems on time scales (see [16,17]) or in second order hamiltonian systems [18]. Moreover, the study of the existence and multiplicity of solutions for impulsive dynamic equations on time scales has also been done by means of varational method(see, for example, [19,20]).…”