Abstract
Cauchy's problem for the equationu xx +λx −1 u x =u t (λ real) was discussed byD. Colton if λ≠−1,−2,−3, ... Now existence and uniqueness theorems and representations of the solutions are given for the cases λ=−1,−2, −3,... The methods ofD. Colton and of this paper are different but the results are similar.
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