Existence of solutions for nonlinear second-order q-difference equations with first-order q-derivatives

Existence of solutions for nonlinear impulsive qk-difference equations with first-order qk-derivatives

In this paper, we study the nonlinear second-order impulsive qk-difference equations with Sturm-Liouville type, in which nonlinear team and impulsive teams are dependent on first-order qk-derivatives. We obtain the existence and uniqueness results of solutions for the problem by Banach’s contraction mapping principle and Schaefer’s fixed point theorems. Finally, we give two examples to demonstr...

q-Karamata functions and second order q-difference equations

In this paper we introduce and study q-rapidly varying functions on the lattice q0 := {qk : k ∈ N0}, q > 1, which naturally extend the recently established concept of q-regularly varying functions. These types of functions together form the class of the so-called q-Karamata functions. The theory of q-Karamata functions is then applied to half-linear q-difference equations to get information abo...

Variational Iteration Method for q-Difference Equations of Second Order

POSITIVE PERIODIC SOLUTIONS FOR HIGHER-ORDER FUNCTIONAL q-DIFFERENCE EQUATIONS

In this paper, using the recently introduced concept of periodic functions in quantum calculus, we study the existence of positive periodic solutions of a certain higher-order functional q-difference equation. Just as for the well-known continuous and discrete versions, we use a fixed point theorem in a cone in order to establish the existence of a positive periodic solution. This paper is dedi...

Existence of Periodic Solutions for Higher-order Nonlinear Difference Equations

In this article, we study a higher-order nonlinear difference equation. By using critical point theory, we establish sufficient conditions for the existence of periodic solutions.