This paper investigates the existence of positive strongly decaying solutions of second-order nonlinear q-difference equation with q-regularly varying coefficients a and b. By means of a fixed point theorem in partially ordered Banach space, necessary and sufficient conditions for the existence of solutions satisfying and as are established. Moreover, with the help of q-regular varying theory, precise asymptotic behaviour of such solutions is described.

中文翻译：

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二阶非线性q-差分方程正强衰减解的存在性

本文研究了具有q-正则变化系数a和b的二阶非线性q-差分方程的正强衰减解的存在性。通过偏序Banach空间中的不动点定理，成立了满足和as的解存在的充要条件。此外，在 q 正则变化理论的帮助下，描述了这种解的精确渐近行为。