Bihari–LaSalle inequality
The Bihari–LaSalle inequality, was proved by the American mathematician
Joseph P. LaSalle in 1949 and by the Hungarian mathematician
Imre Bihari in 1956. It is the following nonlinear generalization of Grönwall's lemma.
Let u and ƒ be non-negative continuous functions defined on the half-infinite ray 0, ∞), and [let w be a continuous non-decreasing function defined on 0, ∞) and w > [0 on. If u satisfies the following integral inequality,
where α is a non-negative constant, then
where the function G is defined by
and G−1 is the inverse function of G and T is chosen so that
