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In this note we establish some results of local existence and uniqueness for the equations u(x, t) = u 0 (x) + t 0 u τ 0 u(x, s)ds, τ dτ, t ≥ 0, x ∈ R, u(x, t) = u 0 (x) + t 0 u 1 τ τ 0 u(x, s)ds, τ dτ, t ≥ 0, x ∈ R and u(x, t) = u 0 (x) + t 0 u τ 0 1 2δ(s) x+δ(s) x−δ(s) and ∂ ∂t u(x, t) = u t 0 1 2δ(s) x+δ(s) x−δ(s) where u 0 e δ are given… (More)

We give a result of local existence and uniqueness for equations of the type ∂ 2 ∂t 2 u(x, t) = k1u ∂ 2 ∂t 2 u(x, t) + k2u(x, t), t where k1 and k2 are given real numbers or real functions ki = ki(x, t). In previous notes we have started the study of a new type of differential equations that we have called self-referred and hereditary (see [4], [5]). The… (More)

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