Multiplicity results for nonlocal critical problems involving Hardy potential in the whole space

2021 ◽  
pp. 1-37
Author(s):  
B. Abdellaoui ◽  
A. Attar ◽  
Y. O. Boukarabila ◽  
E. -H. Laamri
Keyword(s):  
Hardy Potential ◽  
Multiplicity Results ◽  
Whole Space ◽  
Critical Problems

scholarly journals Multiplicity results for Kirchhoff type elliptic problems with Hardy potential

2019 ◽  
Vol 38 (4) ◽  
pp. 31-50
Author(s):  
M. Bagheri ◽  
Ghasem A. Afrouzi
Keyword(s):  
Local Minimum ◽  
Nonlinear Term ◽  
Existence Of Solutions ◽  
Mountain Pass Theorem ◽  
Elliptic Problems ◽  
Mountain Pass ◽  
Hardy Potential ◽  
Multiplicity Results ◽  
Kirchhoff Type ◽  
Minimum Theorem

In this paper, we are concerned with the existence of solutions for fourth-order Kirchhoff type elliptic problems with Hardy potential. In fact, employing a consequence of the local minimum theorem due to Bonanno and mountain pass theorem we look into the existence results for the problem under algebraic conditions with the classical Ambrosetti-Rabinowitz (AR) condition on the nonlinear term. Furthermore, by combining two algebraic conditions on the nonlinear term using two consequences of the local minimum theorem due to Bonanno we ensure the existence of two solutions, applying the mountain pass theorem given by Pucci and Serrin we establish the existence of third solution for our problem.

scholarly journals Existence of three weak solutions for fourth-order elastic beam equations on the whole space

2020 ◽  
Vol 72 (12) ◽  
pp. 1697-1707
Author(s):  
M. R. H. Tavani
Keyword(s):  
Critical Point ◽  
Fourth Order ◽  
Elastic Beam ◽  
Point Theory ◽  
Order Problem ◽  
Multiplicity Results ◽  
Nonlinear Anal ◽  
Beam Equations ◽  
Whole Space ◽  
Fourth Order Problem

UDC 517.9 Multiplicity results for a perturbed fourth-order problem on the real line with a perturbed nonlinear term depending on one real parameter is investigated. Our approach is based on variational methods and critical point theory which are obtained in [G. Bonanno, <em>A critical point theorem via the Ekeland variational principle</em>, Nonlinear Anal., <strong>75</strong>, 2992-3007 (2012)].

A simplified method of emulsion coating and development for quantitative electron microscopic radioautography

1978 ◽  
Vol 36 (2) ◽  
pp. 64-65
Author(s):  
K. Yoshida ◽  
F. Murata ◽  
S. Ohno ◽  
T. Nagata
Keyword(s):  
Mass Production ◽  
Identical Condition ◽  
Microscopic Level ◽  
Electron Microscopic Level ◽  
Electron Microscopic ◽  
Simplified Method ◽  
Complicated Process ◽  
Critical Problems ◽  
Electron Microscopic Radioautography ◽  
Quantitative Radioautography

IntroductionSeveral methods of mounting emulsion for radioautography at the electron microscopic level have been reported. From the viewpoint of quantitative radioautography, however, there are many critical problems in the procedure to produce radioautographs. For example, it is necessary to apply and develop emulsions in several experimental groups under an identical condition. Moreover, it is necessary to treat a lot of grids at the same time in the dark room for statistical analysis. Since the complicated process and technical difficulties in these procedures are inadequate to conduct a quantitative analysis of many radioautographs at once, many factors may bring about unexpected results. In order to improve these complicated procedures, a simplified dropping method for mass production of radioautographs under an identical condition was previously reported. However, this procedure was not completely satisfactory from the viewpoint of emulsion homogeneity. This paper reports another improved procedure employing wire loops.

Coal mining-disturbed land reclamation laws

2020 ◽  
pp. 15-26
Author(s):  
T. V. Galanina ◽  
M. I. Baumgarten ◽  
T. G. Koroleva
Keyword(s):  
Large Scale ◽  
Land Reclamation ◽  
Mining Industry ◽  
Development Program ◽  
Soil Disturbance ◽  
Open Pit ◽  
Open Pit Mining ◽  
Disturbed Land ◽  
Critical Problems ◽  
Production Output

Large-scale mining disturbs wide areas of land. The development program for the mining industry, with an expected considerable increase in production output, aggravates the problem with even vaster territories exposed to the adverse anthropogenic impact. Recovery of mining-induced ecosystems in the mineral-extracting regions becomes the top priority objective. There are many restoration mechanisms, and they should be used in integration and be highly technologically intensive as the environmental impact is many-sided. This involves pollution of water, generation of much waste and soil disturbance which is the most typical of open pit mining. Scale disturbance of land, withdrawal of farming land, land pollution and littering are critical problems to the solved in the first place. One of the way outs is highquality reclamation. This article reviews the effective rules and regulations on reclamation. The mechanism is proposed for the legal control of disturbed land reclamation on a regional and federal level. Highly technologically intensive recovery of mining-induced landscape will be backed up by the natural environment restoration strategy proposed in the Disturbed Land Reclamation Concept.

Inhibiting Factors of Cost Performance in UAE Construction Projects

2020 ◽  
Vol 11 (2) ◽  
Author(s):  
Ahmed Salem Ahmed Marey Alhammadi ◽  
◽  
Aftab Hameed Memon ◽  
Keyword(s):  
Construction Industry ◽  
Construction Projects ◽  
Past Research ◽  
Cost Overrun ◽  
Index Method ◽  
Cost Performance ◽  
Factors Affecting ◽  
Inhibiting Factors ◽  
Critical Problems ◽  
Structured Questionnaire

UAE construction industry frequently faces poor cost performance which commonly known as cost overrun problem. This problem is resulted from several factors and it is important to identify these cost overrun factors in order to avoid and minimize it. Hence, this paper focused on determined the relevancy of factors affecting cost performance in construction projects of UAE. Through a review of past research works conducted globally, 27 factors of cost overrun were listed and used for developing a structured questionnaire. A survey was conducted with 33 practitioners from client, consultant and contractors organizations involved in handling construction projects in UAE. The respondents were requested to state their perception regarding the relevancy of each of the factors that was perceived in context with cost overrun issue using 5-points Likert scale. The responses were analysed using average index method and the results found that all the 27 factors are relevant with construction industry of UAE in causing cost overrun. These factors can be used for further investigation to uncover critical problems of cost overrun.

Some Critical Problems of Botnets

2012 ◽  
Vol 35 (6) ◽  
pp. 1192 ◽  
Author(s):  
Tian-Zuo WANG ◽  
Huai-Min WANG ◽  
Bo LIU ◽  
Pei-Chang SHI
Keyword(s):  
Critical Problems

‘Wisselbare Woorde’

2018 ◽  
Author(s):  
Carrol Clarkson
Keyword(s):  
South Africa ◽  
Freedom Of Expression ◽  
The Other ◽  
Frantz Fanon ◽  
Politics Of Representation ◽  
Black Consciousness ◽  
Nadine Gordimer ◽  
Contact Zones ◽  
Critical Problems ◽  
Ethics And Politics

Carrol Clarkson’s chapter wrestles with the contentious question of Coetzee’s relation to the Black Consciousness Movement in South Africa of the 1970s and early 1980s, which took its philosophical bearings from Frantz Fanon and found expression in the writings of Steve Biko. Clarkson focuses on the ways in which Coetzee departed from the ideas about writing and resistance that were circulating in his contemporary South Africa, particularly as articulated by novelist Nadine Gordimer. Clarkson discusses two related literary-critical problems: an ethics and politics of representation, and an ethics and politics of address, showing how Coetzee explores a tension between freedom of expression and responsibility to the other. In the slippage from saying to addressing we are led to further thought about modes and sites of consciousness—and hence accountabilities—in the interlocutory contact zones of the post-colony. The chapter invites a sharper appreciation of what a postcolonial philosophy might be.

scholarly journals Multiple positive solutions for nonlocal elliptic problems involving the Hardy potential and concave–convex nonlinearities

2020 ◽  
pp. 2050008
Author(s):  
Shaya Shakerian
Keyword(s):  
Variational Methods ◽  
Bounded Domain ◽  
Positive Solutions ◽  
Variational Approach ◽  
Nehari Manifold ◽  
Multiple Positive Solutions ◽  
Hardy Potential ◽  
Smooth Bounded Domain ◽  
Existence And Multiplicity ◽  
The Nehari Manifold

In this paper, we study the existence and multiplicity of solutions for the following fractional problem involving the Hardy potential and concave–convex nonlinearities: [Formula: see text] where [Formula: see text] is a smooth bounded domain in [Formula: see text] containing [Formula: see text] in its interior, and [Formula: see text] with [Formula: see text] which may change sign in [Formula: see text]. We use the variational methods and the Nehari manifold decomposition to prove that this problem has at least two positive solutions for [Formula: see text] sufficiently small. The variational approach requires that [Formula: see text] [Formula: see text] [Formula: see text], and [Formula: see text], the latter being the best fractional Hardy constant on [Formula: see text].

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