Related papers: On three problems of Y.--G. Chen
We claim to resolve the P=?NP problem via a formal argument for P=NP.
This note contains a short proof of the functional equation for the zeta function.
In this small note we ask several questions which are relevant to the construction of the self-consistent neutrino theory of light. The previous confusions in such attempts are explained in the more detailed publication.
We obtain, by using the Leggett-Williams fixed point theorem, sufficient conditions that ensure the existence of at least three positive solutions to some $p$-Laplacian boundary value problems on time scales.
Let $A$ be a real $n\times n$ matrix and $z,b\in \mathbb R^n$. The piecewise linear equation system $z-A\vert z\vert = b$ is called an \textit{absolute value equation}. We consider two solvers for this problem, one direct, one…
We refine a result of W.P. Li and Wang on the values of the form $ \lambda_1p_1 + \lambda_2p_2^{2} + \lambda_3p_3^{2} + \mu_1 2^{m_1} +...+ \mu_s 2^{m_s}, $ where $p_1,p_2,p_3$ are prime numbers, $m_1,..., m_s$ are positive integers,…
We study the monotonicity behavior of three slightly differently defined additive representation functions (as initiated by Erd\H{o}s, S\'{a}rk\"{o}zy and S\'{o}s), answering one open question and another one partially, and give a slightly…
This article concerns on the existence of multiple solutions for a new Kirchhoff-type problem with negative modulus. We prove that there exist three nontrivial solutions when the parameter is enough small via the variational methods and…
In this paper, by making use of one of Chen's theorems and the method of mathematical analysis, we refine Edwards-Child's inequality and solve a conjecture posed by Liu.
We give a different proof of a theorem of W. Gangbo and A. Swiech on the short time existence of solutions of the master equation.
In this paper we discuss the existence and regularity of solutions of fractional Lane-Emden systems with weights.
Some simple facts are proved ruling the Collatz tree and the chains of vertices appearing in it, leading to the reduction of the number of significant elements appearing in the tree. Although the Collatz conjecture remains open, these fact…
This note is the written version of conversations with young colleagues on unofficial history, general ideas, unexpected facts and open problems concerning tilting theory.
In this paper, the author represent a unification and extension of concepts previously studied by several authors. By establish connections between the chain condition, selectively star-ccc properties and star-Lindel\"of properties, the…
In this paper we study an elliptic variational problem regarding the $p$-fractional Laplacian in $\mathbb{R}^N$ on the basis of recent result \cite{Ha1}, which generalizes the nice work \cite{AT,AP,XZR1}, and then give some sufficient…
In this paper we give positive answers for two open questions on extension bundles over weighted projective lines, raised by Kussin, Lenzing and Meltzer in the paper ``Triangle singularities, ADE-chains and weighted projective lines''.
We respond to invalid criticism in the recent Comment by Schneider et al. [arXiv:1407.4127v1]
The essential elements in my way of fitting the kappa reviewed. A number of incorrect claims made by Takamatsu are clarified and corrected.
We consider a nonlinear Neumann problem driven by the $p$-Laplacian. In the reaction term we have the competing effects of a singular and a convection term. Using a topological approach based on the Leray-Schauder alternative principle…
Considering the equation $$a^x+b^y = c^z,$$ Le gives an upper bound on the number of solutions $(x,y,z)$, and a bound on $z$. Here we give slight improvements to these results, also removing the restriction that $a$, $b$, $c$ be squarefree.