Nguyen Van Thin

On existence solution for Schrödinger–Kirchhoff-type equations involving the fractional p-Laplacian in

ABSTRACT The aim of this paper is to study the existence solution for Schrödinger–Kirchhoff-type equations involving nonlocal p-fractional Laplacian where is a real positive parameter, is a continuous function, is a singular kernel function, is a nonlocal fractional operator, with f is a Carathéodory function on satisfying the Ambrosetti–Rabinowitz-type condition. Using Mountain Pass Theorem, we obtain the existence of above equations. Our result is a extension the problem studied by Pucci–Xiang–Zhang [1].

Schmidt's subspace theorem for moving hypersurface targets

Abstract It was discovered that there is a formal analogy between Nevanlinna theory and Diophantine approximation. Via Vojtas dictionary, the Second Main Theorem in Nevanlinna theory corresponds to Schmidts Subspace Theorem in Diophantine approximation. Recently, Cherry, Dethloff, and Tan ( arXiv:1503.08801v2 [math.CV] ) obtained a Second Main Theorem for moving hypersurfaces intersecting projective varieties. In this paper, we shall give the counterpart of their Second Main Theorem in Diophantine approximation.

A modification of the Nevanlinna–Cartan theory for holomorphic curve

In this paper, we prove some fundamental theorems for holomorphic curves on intersecting a finite set of fixed hyperplanes in general position in with modified counting and characteristic functions.

Normal family of meromorphic functions sharing holomorphic functions and the converse of the bloch principle

Abstract In 1996, C. C. Yang and P. C. Hu [8] showed that: Let f be a transcendental meromorphic function on the complex plane, and a ≠ 0 be a complex number; then assume that n ≥ 2, n 1 , …, n k are nonnegative integers such that n 1 + ⋯ + n k ≥ 1 ; thus f n ( f ′ ) n 1 ⋯ ( f ( k ) ) n k − a has infinitely zeros. The aim of this article is to study the value distribution of differential polynomial, which is an extension of the result of Yang and Hu for small function and all zeros of f having multiplicity at least k ≥ 2. Namely, we prove that f n ( f ′ ) n 1 ⋯ ( f ( k ) ) n k − a ( z ) has infinitely zeros, where f is a transcendental meromorphic function on the complex plane whose all zeros have multiplicity at least k ≥ 2, and a ( z ) ≡ 0 is a small function of f and n ≥ 2, n 1 ,…, n k are nonnegative integers satisfying n 1 +…+ n k ≥ 1. Using it, we establish some normality criterias for a family of meromorphic functions under a condition where differential polynomials generated by the members of the family share a holomorphic function with zero points. The results of this article are supplement of some problems studied by J. Yunbo and G. Zongsheng [6], and extension of some problems studied X. Wu and Y. Xu [10]. The main result of this article also leads to a counterexample to the converse of Blochs principle.