Given a Banach space E, it is proved that any function u in C2([a; b];E) verifies a Lyapunov inequality. The provided constant is sharp. Several applications are included

Constantin P. Niculescu

Given a Banach space E, it is proved that any function u in C2([a, b], E) verifies the inequality max {‖u(a) ‖ , ‖u(b)‖}+ b − a 4 ∫ b a ‖u′′(t) ‖ dt ≥ sup t∈[a,b] ‖u(t) ‖. The constant (b − a)/4 is sharp. Several applications are included

A NEW LOOK AT THE LYAPUNOV INEQUALITY

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