Displaying similar documents to “Amenability and weak amenability of Lipschitz operators algebras.”

An abstract nonlinear second order differential equation

Jan Bochenek (1991)

Annales Polonici Mathematici

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By using the theory of strongly continuous cosine families of linear operators in Banach space the existence of solutions of a semilinear second order differential initial value problem (1) as well as the existence of solutions of the linear inhomogeneous problem corresponding to (1) are proved. The main result of the paper is contained in Theorem 5.

On a Theorem of Mierczyński

Gerd Herzog (1998)

Colloquium Mathematicae

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We prove that the initial value problem x’(t) = f(t,x(t)), x ( 0 ) = x 1 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.