Linear integral equations in the space of regulated functions.
Linear operators in the space of regulated functions
Representation of bounded and compact linear operators in the Banach space of regulated functions is given in terms of Perron-Stieltjes integral.
Linear operators satisfying the chain rule.
Linear Stieltjes integral equations in Banach spaces
Fundamental results concerning Stieltjes integrals for functions with values in Banach spaces have been presented in [5]. The background of the theory is the Kurzweil approach to integration, based on Riemann type integral sums (see e.g. [3]). It is known that the Kurzweil theory leads to the (non-absolutely convergent) Perron-Stieltjes integral in the finite dimensional case. Here basic results concerning equations of the form x(t) = x(a) +at [A(s)]x(s) +f(t) - f(a) are presented on the basis of...
Linear Volterra-Stieltjes integral equations in the sense of the Kurzweil-Henstock integral
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.
Lineární závislost funkcí jedné reálné proměnné
Lipschitz Classes and Restrictions of Fourier Transforms.
Lipschitz conditions on the modulus of a harmonic function.
Lipschitz differences and Lipschitz functions
Lipschitz extensions of convex-valued maps
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 .
Lipschitz functions with unexpectedly large sets of nondifferentiability points.
Lipschitz r-continuity of the approximative subdifferential of a convex function.
Lipschitz regularity and approximate differentiability of the Diperna-Lions flow
Lipschitzian superposition operators on metric semigroups and abstract convex cones of mappings of finite -variation.
Littlewood's inequality for -bimeasures.
lnfinitely many solutions for fractional Schrödinger equations with perturbation via variational methods
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.
Local and global solutions of well-posed integrated Cauchy problems
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.
Local and global -cone porosity
Local characterizations of Darboux Baire 1 functions
Local Field Singular Integrals with Complex Homogeneity.