A family of nonlinear difference equations: existence, uniqueness, and asymptotic behavior of positive solutions

摘要

We study solutions of certain nonhomogeneous nonlinear second order difference equations. Depending on one's standpoint, such equations originate from orthogonal polynomials associated with certain Shohat-Freud-type exponential weight functions or from Painlevé's discrete equation #1, that is d-P_I.