The existence of meromorphic solutions of non-linear complex difference equations is widely considered recently by applying the difference analogues of Nevanlinna theory, where the main purpose is to describe the existence or expressions of their transcendental meromorphic solutions. In this paper, we continue to consider meromorphic solutions of some complex difference equations or systems using novel methods of proof.
In this paper, the existence, uniqueness, and stability of (weighted) Stepanov-like pseudo almost automorphic solutions are investigated for the non-autonomous Oseen–Navier–Stokes equations (ONSE) in an exterior domain. Our method is based on the one hand on a combination of differential inequalities and interpolations functors for the case of linearized equations, and on the other hand on fixed-point arguments for semilinear equations.
Let 1 < p <= 2. Using the layer potential method, we establish the unique solvability in L-p-spaces of the Schr & ouml;dinger equation-triangle u+Vu = 0 on a Lipschitz domain subject to a Robin boundary condition. The potential V belongs to the reverse H & ouml;lder class. The case of C-1-domains is also discussed.
The Hardy-Hilbert integral inequality has been the subject of extensive study in recent decades. In this article, we present a two-parameter exponential generalization of this inequality. The associated constant factor involves the upper incomplete gamma function. Interestingly, it can also be expressed in terms of the classical error function. Through precise analysis, we prove the optimality of this constant. We then derive several integral inequalities of various types, some involving primitive functions, while others incorporating auxiliary functions.
We investigate the complex Monge-Amp & egrave;re operator on a bounded strongly pseudoconvex domain of a closed, connected, singular, and locally irreducible complex-analytic subvariety. We first examine the classes epsilon(p) for p > 0 and establish a characterization of their images under the complex Monge-Amp & egrave;re operator. This result answers a question posed by N. Q. Dieu, T. V. Long. We then turn to the weighted energy classes epsilon(chi) (ohm), consisting of negative plurisubharmonic functions with finite chi-energy, and provide a precise characterization of their images under the complex Monge-Amp & egrave;re operator, where chi is a convex increasing function satisfying chi(0) = 0 and chi(-infinity) = -infinity.
