An analytic function f in the unit disc belongs to F(p,q,s), if

is uniformly bounded for all a ∈ . Here is the Green function of , and φa(z)=(a−z)/(1−āz). It is shown that for 0 < γ < ∞ and |w|=1 the singular inner function exp(γ(z+w)/(z−w)) belongs to F(p,q,s), 0<s≤1, if and only if . Moreover, it is proved that, if 0<s<1, then an inner function belongs to the Möbius invariant Besov-type space for some (equivalently for all) p > max{s,1−s} if and only if it is a Blaschke product whose zero sequence {zn} satisfies .

We prove that if two transcendental meromorphic functions share all limit values from a set of positive linear measure on a rectifiable Jordan arc, then they share all limit values.

This paper is concerned with a boundary-value problem on the half-line for nonlinear two-dimensional delay differential systems with positive delays. A theorem is established, which provides sufficient conditions for the existence of positive solutions. The application of this theorem to the special case of second-order nonlinear delay differential equations is given. Also, the application of the theorem to two-dimensional Emden–Fowler-type delay differential systems with constant delays is presented. Moreover, some general examples demonstrating the applicability of the theorem are included.

The upper and lower solutions method and Leray–Schauder degree theory are employed to establish the existence result for a class of nonlinear third-order two-point boundary-value problems with a sign-type Nagumo condition.

Theorems on the Fredholm alternative and well-posedness of the characteristic initial-value problem

are established, where l : C(;ℝ) is a linear bounded operator, q ∈ L(;ℝ), ϕ:[a,b]→ℝ, ψ:[c,d]→ℝ are absolutely continuous functions and =[a,b]×[c,d]. Some solvability conditions of the problem considered are also given.

We present conditions guaranteeing the existence of non-trivial unstable sets for compact invariant sets in semiflows with certain compactness conditions, and then establish the existence of such unstable sets for an unstable equilibrium or a minimal compact invariant set, not containing equilibria, in an essentially strongly order-preserving semiflow. By appealing to the limit-set dichotomy for essentially strongly order-preserving semiflows, we prove the existence of an orbit connection from an equilibrium to a minimal compact invariant set, not consisting of equilibria. As an application, we establish a new generic convergence principle for essentially strongly order-preserving semiflows with certain compactness conditions.

We use the compensated compactness method coupled with some basic ideas of kinetic formulation developed by Lions, Perthame, Souganidis and Tadmor to give a refined proof for the existence of global bounded entropy solutions to the Le Roux system. This new method of the reduction of Young measures can be applied to solve other problems.