The averaging principle in the case of the Cauchy problem for quasilinear parabolic equations with variable principal part.
Levenshtam, V.B. (2000)
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Levenshtam, V.B. (2000)
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Hakl, R. (1999)
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We prove that the initial value problem x’(t) = f(t,x(t)), is uniquely solvable in certain ordered Banach spaces if f is quasimonotone increasing with respect to x and f satisfies a one-sided Lipschitz condition with respect to a certain convex functional.