scholarly journals Three solutions for a nonlocal problem with critical growth

2019 ◽  
Vol 469 (2) ◽  
pp. 841-851
Author(s):  
Natalí Ailín Cantizano ◽  
Analía Silva
Keyword(s):  
Nonlocal Problem ◽  
Critical Growth ◽  
Three Solutions

scholarly journals Optimal solvability for a nonlocal problem at critical growth

2018 ◽  
Vol 264 (3) ◽  
pp. 2242-2269 ◽  
Author(s):  
Lorenzo Brasco ◽  
Marco Squassina
Keyword(s):  
Nonlocal Problem ◽  
Critical Growth

scholarly journals The Nehari manifold for indefinite Kirchhoff problem with Caffarelli-Kohn-Nirenberg type critical growth

2021 ◽  
pp. 1-30
Author(s):  
David G. Costa ◽  
João Marcos Do Ó ◽  
Pawan K. Mishra
Keyword(s):  
Continuous Function ◽  
Positive Solutions ◽  
Nonlocal Problem ◽  
Nehari Manifold ◽  
Critical Growth ◽  
Positive Real ◽  
Alpha Beta ◽  
The Nehari Manifold ◽  
Kirchhoff Model ◽  
Kirchhoff Problem

In this paper we study the following class of nonlocal problem involving Caffarelli-Kohn-Nirenberg type critical growth $$ L(u)-\lambda h(x)|x|^{-2(1+a)}u=\mu f(x)|u|^{q-2}u+|x|^{-pb}|u|^{p-2}u\quad \text{in } \mathbb R^N, $$% where $h(x)\geq 0$, $f(x)$ is a continuous function which may change sign, $\lambda, \mu$ are positive real parameters and $1< q< 2< 4< p=2N/[N+2(b-a)-2]$, $0\leq a< b< a+1< N/2$, $N\geq 3$. Here $$ L(u)=-M\left(\int_{\mathbb R^N} |x|^{-2a}|\nabla u|^2dx\right)\mathrm {div} \big(|x|^{-2a}\nabla u\big) $$ and the function $M\colon \mathbb R^+_0\to\mathbb R^+_0$ is exactly the Kirchhoff model, given by $M(t)=\alpha+\beta t$, $\alpha, \beta> 0$. The above problem has a double lack of compactness, firstly because of the non-compactness of Caffarelli-Kohn-Nirenberg embedding and secondly due to the non-compactness of the inclusion map $$u\mapsto \int_{\mathbb R^N}h(x)|x|^{-2(a+1)}|u|^2dx,$$ as the domain of the problem in consideration is unbounded. Deriving these crucial compactness results combined with constrained minimization argument based on Nehari manifold technique, we prove the existence of at least two positive solutions for suitable choices of parameters $\lambda$ and $\mu$.

Effects of Image Upload on Social Media as Media Promotion in Journal Publishers

CCIT Journal ◽  
2020 ◽  
Vol 13 (1) ◽  
pp. 20-31
Author(s):  
Untung Rahardja ◽  
Ani Wulandari ◽  
Marviola Hardini
Keyword(s):  
Social Media ◽  
Digital Media ◽  
Digital Content ◽  
Three Solutions ◽  
Conventional Process ◽  
Promotion System

Digital content is content in various formats, whether written, image, video, audio or combination so that it can be read, displayed or played by a computer and easily sent or hared through digital media. Digital content has abundant benefits, especially in the field of promotion. Where when a place of business or a body wants to introduce a product or service that is owned, it definitely requires content such as images as a promotional media. However, if you have to distribute posters to everyone you meet, it is not in line with current technological advancements because you are still using a conventional process. Therefore, to overcome this problem, social media can be used to process digital content easily and quickly. In this study, there are 3 (three) problems that will be overcome by 2 (two) methods, and 3 (three) solutions are produced. The advantage of digital content in social media is that it can be accessed anytime and anywhere, so it is concluded that the use of digital content in social media is able to overcome problems and is a creativepreneur effort found in the promotion system of a journal publisher.   Keywords—Digital Content, Creativepreneur, ATT Journal, Social Media

High Resolution Displacement of Functional Groups onto Fluorocarbon Resin Surface by Using ArF Excimer Laser

1996 ◽  
Vol 451 ◽  
Author(s):  
T. Shimizu ◽  
M. Murahara
Keyword(s):  
Contact Angle ◽  
High Resolution ◽  
Laser Beam ◽  
Thin Layer ◽  
Functional Groups ◽  
Excimer Laser ◽  
Laser Fluence ◽  
Large Area ◽  
Three Solutions ◽  
Arf Excimer Laser

ABSTRACTA Fluorocarbon resin surface was selectively modified by irradiation with a ArF laser beam through a thin layer of NaAlO2, B(OH)3, or H2O solution to give a hydrophilic property. As a result, with low fluence, the surface was most effectively modified with the NaAlO2 solution among the three solutions. However, the contact angle in this case changed by 10 degrees as the fluence changed only 1mJ/cm2. When modifying a large area of the surface, high resolution displacement could not be achieved because the laser beam was not uniform in displacing functional groups. Thus, the laser fluence was successfully made uniform by homogenizing the laser beam; the functional groups were replaced on the fluorocarbon resin surface with high resolution, which was successfully modified to be hydrophilic by distributing the laser fluence uniformly.

scholarly journals Existence and Concentration Behavior of Solutions of the Critical Schrödinger–Poisson Equation in R3

Mathematics ◽  
2021 ◽  
Vol 9 (5) ◽  
pp. 464
Author(s):  
Jichao Wang ◽  
Ting Yu
Keyword(s):  
Poisson Equation ◽  
Existence Result ◽  
Critical Growth ◽  
Singularly Perturbed ◽  
Singularly Perturbed Problem ◽  
Number Of Solutions ◽  
Concentration Behavior ◽  
The Relationship ◽  
Concentration Phenomenon

In this paper, we study the singularly perturbed problem for the Schrödinger–Poisson equation with critical growth. When the perturbed coefficient is small, we establish the relationship between the number of solutions and the profiles of the coefficients. Furthermore, without any restriction on the perturbed coefficient, we obtain a different concentration phenomenon. Besides, we obtain an existence result.

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