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On conjugacy of second-order half-linear differential equations on the real axis

Some conjugacy criteria are given for the equation ( |u′|α sgn u′ )′ + p(t)|u| sgn u = 0, where p : R → R is a locally integrable function and α > 0, which generalise and supplement results known in the existing literature. Illustrative examples justifying applicability of the main results are given, as well. The results obtained are new even for linear differential equations, i.e., if α = 1.