We denote by Λβ(λ), β>0, the Lorentz space equipped with the (quasi) norm ∥f∥Λβ(λ):=(∫10(f∗(t)tλ(1t))βdtt)1β for a function f on [0,1] and with λ positive and equipped with some additional growth properties. Some ...

We denote by Λβ(λ), β>0, the Lorentz space equipped with the (quasi) norm ∥f∥Λβ(λ):=(∫10(f∗(t)tλ(1t))βdtt)1β for a function f on [0,1] and with λ positive and equipped with some additional growth properties. Some ...

Some new Hardy-type inequalities for Hardy-Volterra integral operators are proved and discussed. The case 1 < q < p < 1 is considered and the involved kernels satisfy conditions, which are less restrictive than the usual ...

The DSM (dynamical systems method) version of the Newton’s method is for solving operator equation F(u) = f in Banach spaces is discussed. If F is a global homeomorphism of a Banach space X onto X, that is continuously ...

A generalized Toda Lattice equation is considered. The associated linear problem (Lax representation) is found. For simple case N = 3 the -function Hirota form is presented that allows to construct an exast solutions of ...

In the context of the so-called Gauss–Bonnet gravity, where the gravitational action includes function of the Gauss–Bonnet invariant, we study cosmological solutions, especially the well-known ΛCDM model. It is shown ...

Some exact solutions of the (2+1)-dimensional integrable classical con-tinuous isotropic Heisenberg spin chain (the M-XX equation) are obtained by using Hirota’s method. These solutions are characterized by an ...