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In 1990, Hönig proved that the linear Volterra integral equation
where the functions are Banach space-valued and is a Kurzweil integrable function defined on a compact interval of the real line , admits one and only one solution in the space of the Kurzweil integrable functions with resolvent given by the Neumann series. In the present paper, we extend Hönig’s result to the linear Volterra-Stieltjes integral equation
in a real-valued context.
We obtain Liouville type theorems for mappings with bounded -distorsion between
Riemannian manifolds. Besides these mappings, we introduce and study a new class, which
we call mappings with bounded -codistorsion.
Si dimostra che ogni funzione multivoca lipschitziana con costante di Lipschitz , definita su un sottoinsieme di uno spazio di Hilbert a valori compatti e convessi in , può essere estesa su tutto ad una funzione multivoca lipschitziana con costante minore di 7 nM. In generale, non esistono invece estensioni aventi la stessa costante di Lipschitz .
We give a geometric characterization of the convex subsets of a Banach space with the property that for any two convex continuous functions on this set, if their sum is Lipschitz, then the functions must be Lipschitz. We apply this result to the theory of Δ-convex functions.
Using variational methods, we investigate the solutions of a class of fractional Schrödinger equations with perturbation. The existence criteria of infinitely many solutions are established by symmetric mountain pass theorem, which extend the results in the related study. An example is also given to illustrate our results.
We study the local well-posed integrated Cauchy problem
, v(0) = 0, t ∈ [0,κ),
with κ > 0, α ≥ 0, and x ∈ X, where X is a Banach space and A a closed operator on X. We extend solutions increasing the regularity in α. The global case (κ = ∞) is also treated in detail. Growth of solutions is given in both cases.
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