Results 101 to 110 of about 764,891 (332)
A note on Sierpiński problem related to triangular numbers [PDF]
arXiv, 2008 In this note we show that the system of equations t_{x}+t_{y}=t_{p},\quad t_{y}+t_{z}=t_{q},\quad t_{x}+t_{z}=t_{r}, where $t_{x}=x(x+1)/2$ is a triangular number, has infinitely many solutions in integers. Moreover we show that this system has rational three-parametric solution.
arxiv
Existence of infinitely many solutions for fourth-order equations depending on two parameters
Electronic Journal of Differential Equations, 2017 By using variational methods and critical point theory, we establish the existence of infinitely many classical solutions for a fourth-order differential equation. This equation has nonlinear boundary conditions and depends on two real parameters.
Armin Hadjian, Maryam Ramezani
doaj
Infinitely many solutions for Hamiltonian system with critical growth
Advances in Nonlinear AnalysisIn this article, we consider the following elliptic system of Hamiltonian-type on a bounded domain:−Δu=K1(∣y∣)∣v∣p−1v,inB1(0),−Δv=K2(∣y∣)∣u∣q−1u,inB1(0),u=v=0on∂B1(0),\left\{\begin{array}{ll}-\Delta u={K}_{1}\left(| y| ){| v| }^{p-1}v,\hspace{1.0em ...
Guo Yuxia, Hu Yichen
doaj +1 more source
Infinitely many weak solutions for fourth-order equations depending on two parameters
Boletim da Sociedade Paranaense de Matemática, 2018 In this paper, by employing Ricceri variational principle, we prove the existence of infinitely many weak solutions for fourth-order problems depending on two real parameters.
Saeid Shokooh +2 more
doaj +1 more source
Omnidirectional Transmissive Acoustic Metasurfaces Based on Goldberg Polyhedra
Advanced Functional Materials, EarlyView.This study introduces omnidirectional acoustic metasurfaces capable of manipulating wavefronts in multiple arbitrary directions simultaneously. A full‐stack pipeline for design, optimization, and fabrication is presented to construct near‐spherical holograms based on Goldberg polyhedra.
Andrea Achilleos +3 more
wiley +1 more source
Cauchy problem for dissipative Hölder solutions to the incompressible Euler equations [PDF]
arXiv, 2013 We consider solutions to the Cauchy problem for the incompressible Euler equations on the 3-dimensional torus which are continuous or H\"older continuous for any exponent $\theta<\frac{1}{16}$. Using the techniques introduced in \cite{DS12} and \cite{DS12H}, we prove the existence of infinitely many (H\"older) continuous initial vector fields starting ...
arxiv
Advanced Functional Materials, EarlyView.Synthetic cells are engineered herein to respond to an external chemical messenger by the activation of intracellular catalysis. The chemical messenger molecules are catalytically generated by an extracellular enzyme or a mineral surface, whereas the intracellular catalysis emerges via direct enzyme activation or via protein refolding.
Dante G. Andersen +5 more
wiley +1 more source
Infinitely many solutions for Kirchhoff-type problems depending on a parameter
Electronic Journal of Differential Equations, 2016 In this article, we study a Kirchhoff type problem with a positive parameter $\lambda$, $$\displaylines{ -K\Big( \int_{\Omega }|\nabla u|^{2}dx\Big) \Delta u=\lambda f(x,u) , \quad \text{in } \Omega , \cr u=0, \quad \text{on } \partial \Omega , }$
Juntao Sun, Yongbao Ji, Tsung-fang Wu
doaj
Existence of infinitely many solutions for the fractional Schr\"odinger- Maxwell equations
, 2015 In this paper, by using variational methods and critical point theory, we shall mainly study the existence of infinitely many solutions for the following fractional Schr\"odinger-Maxwell equations $$( -\Delta )^{\alpha} u+V(x)u+\phi u=f(x,u), \hbox{in } \
Wei, Zhongli
core
Existence of infinitely many solutions for a forward backward heat equation [PDF]
, 1983 Klaus Höllig
openalex +1 more source