Extreme and moderate solutions of nonoscillatory second order half-linear differential equations

. An existence and asymptotic theory is built for second order half-linear differential equations of the form where α > 0 is constant and p ( t ) and q ( t ) are positive continuous functions on [ a, ∞ ) , in which a crucial role is played by a pair of the generalized Riccati differential equations associated with (A). An essential part of the theory is the construction of nonoscillatory solutions x ( t ) of (A) enjoying explicit exponential-integral representations in terms of solutions u ( t ) of (R1) or in terms of solutions v ( t ) of (R2).