LVIV, Ukraine—In late February, Russian President Vladimir Putin unleashed a military offensive designed to swiftly outmaneuver Ukraine’s defenders, oust the country’s government and win control over his smaller neighbor. Ten days later, Mr. Putin’s armies are struggling to gain momentum.

Combat-hardened Ukrainian troops, armed with weapons from the U.S., Britain and elsewhere, have managed to slow and in some cases halt Russian advances by taking advantage of strong morale, a deep, home-team knowledge of the battlefield and Russian shortcomings in logistics and tactics.

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