The aim of this paper is to prove the existence of one or multiple solutions of nonlinear difference equations coupled to a general set of boundary conditions.Before to do this,we construct a discrete operator whose f...The aim of this paper is to prove the existence of one or multiple solutions of nonlinear difference equations coupled to a general set of boundary conditions.Before to do this,we construct a discrete operator whose fixed points coincide with the solutions of the problem we are looking for.Moreover,we introduce a strong positiveness condition on the related Green's function that allows us to construct suitable cones where to apply adequate fixed point theorems.Once we have the general existence result,we deduce,as a particular case,the existence of solutions of a second order difference equation with nonlocal perturbed Dirichlet conditions.展开更多
Infrared imaging is a crucial technique in a multitude of applications,including night vision,autonomous vehicle navigation,optical tomography,and food quality control.Conventional infrared imaging technologies,howeve...Infrared imaging is a crucial technique in a multitude of applications,including night vision,autonomous vehicle navigation,optical tomography,and food quality control.Conventional infrared imaging technologies,however,require the use of materials such as narrow bandgap semiconductors,which are sensitive to thermal noise and often require cryogenic cooling.We demonstrate a compact all-optical alternative to perform infrared imaging in a metasurface composed of GaAs semiconductor nanoantennas,using a nonlinear wave-mixing process.We experimentally show the upconversion of short-wave infrared wavelengths via the coherent parametric process of sum-frequency generation.In this process,an infrared image of a target is mixed inside the metasurface with a strong pump beam,translating the image from the infrared to the visible in a nanoscale ultrathin imaging device.Our results open up new opportunities for the development of compact infrared imaging devices with applications in infrared vision and life sciences.展开更多
基金partially supported by Xunta de Galicia(Spain),project EM2014/032 and AIE,Spain and FEDER,grant MTM2016-75140-Psupported by the Bulgarian National Science Fundation under Project DN 12/4“Advanced Analytical and Numerical Methods for Nonlinear Differential Equations with Applications in Finance and Environmental Pollution”,2017。
文摘The aim of this paper is to prove the existence of one or multiple solutions of nonlinear difference equations coupled to a general set of boundary conditions.Before to do this,we construct a discrete operator whose fixed points coincide with the solutions of the problem we are looking for.Moreover,we introduce a strong positiveness condition on the related Green's function that allows us to construct suitable cones where to apply adequate fixed point theorems.Once we have the general existence result,we deduce,as a particular case,the existence of solutions of a second order difference equation with nonlocal perturbed Dirichlet conditions.
基金The authors acknowledge the use of the Australian National Fabrication Facility(ANFF),ACT Node.Rocio CamachoMorales acknowledges a grant from the Consejo Nacional de Ciencia y Tecnología(CONACYT),MexicoNikolay Dimitrov and Lyubomir Stoyanov acknowledge a grant from the EU Marie-Curie RISE program NOCTURNO+1 种基金Mohsen Rahmani acknowledges support from the UK Research and Innovation Future Leaders Fellowship(MR/T040513/1)Dragomir N.Neshev acknowledges a grant from the Australian Research Council(CE20010001,DP190101559).
文摘Infrared imaging is a crucial technique in a multitude of applications,including night vision,autonomous vehicle navigation,optical tomography,and food quality control.Conventional infrared imaging technologies,however,require the use of materials such as narrow bandgap semiconductors,which are sensitive to thermal noise and often require cryogenic cooling.We demonstrate a compact all-optical alternative to perform infrared imaging in a metasurface composed of GaAs semiconductor nanoantennas,using a nonlinear wave-mixing process.We experimentally show the upconversion of short-wave infrared wavelengths via the coherent parametric process of sum-frequency generation.In this process,an infrared image of a target is mixed inside the metasurface with a strong pump beam,translating the image from the infrared to the visible in a nanoscale ultrathin imaging device.Our results open up new opportunities for the development of compact infrared imaging devices with applications in infrared vision and life sciences.
