Properties of critical and subcritical second order self-adjoint linear equations

Abstract

Abstract We discuss critical and subcritical linear second-order difference equations, and we observe several identities and inequalities which such equations satisfy depending on their coefficients. Later, we investigate the limit behaviour depending on the coefficients of solutions and of the sequences which appear when finding said solutions. We will see that certain identity is preserved in limit under weaker assumptions. Finally, we investigate a class of fourth-order linear difference equations and show that they are always 1-critical.