Impulsive quantum $(p,q)$-difference equations
Thana Nuntigrangjana, Sasitorn Putjuso, Sotiris K. Ntouyas, Jessada Tariboon
Abstract
Abstract In this paper we study quantum $(p,q)$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>(</mml:mo><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>q</mml:mi><mml:mo>)</mml:mo></mml:math> -difference equations with impulse and initial or boundary conditions. We consider first order impulsive $(p,q)$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>(</mml:mo><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>q</mml:mi><mml:mo>)</mml:mo></mml:math> -difference boundary value problems and second order impulsive $(p,q)$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>(</mml:mo><mml:mi>p</mml:mi><mml:mo>,</mml:mo><mml:mi>q</mml:mi><mml:mo>)</mml:mo></mml:math> -difference initial value problems. Existence and uniqueness results are proved via Banach’s fixed point theorem.