scholarly journals A Schechter type critical point result in annular conical domains of a Banach space and applications

2016 ◽  
Vol 36 (7) ◽  
pp. 3775-3789 ◽  
Author(s):  
Hannelore Lisei ◽  
Radu Precup ◽  
Csaba Varga
Keyword(s):  
Banach Space ◽  
Critical Point ◽  
Critical Point Result

scholarly journals Existence results for nonlinear elliptic problems on fractal domains

2016 ◽  
Vol 5 (1) ◽  
Author(s):  
Massimiliano Ferrara ◽  
Giovanni Molica Bisci ◽  
Dušan Repovš
Keyword(s):  
Weak Solution ◽  
Dirichlet Problem ◽  
Critical Point ◽  
Elliptic Problems ◽  
Open Interval ◽  
Existence Results ◽  
Nonlinear Elliptic Problems ◽  
Nonlinear Elliptic ◽  
Fractal Domains ◽  
Critical Point Result

AbstractSome existence results for a parametric Dirichlet problem defined on the Sierpiński fractal are proved. More precisely, a critical point result for differentiable functionals is exploited in order to prove the existence of a well-determined open interval of positive eigenvalues for which the problem admits at least one non-trivial weak solution.

scholarly journals A deformation lemma and some critical point theorems

1991 ◽  
Vol 43 (1) ◽  
pp. 161-168 ◽  
Author(s):  
Yihong Du
Keyword(s):  
Banach Space ◽  
Critical Point ◽  
Real Banach Space ◽  
Deformation Lemma ◽  
Palais Smale Condition ◽  
Critical Point Theorems

A new deformation lemma for functions satisfying the Palais-Smale condition on a real Banach space is obtained. This is used to deduce some critical point theorems which are extensions of some well known results.

Three Weak Solutions for Nonlocal Fractional Equations

2014 ◽  
Vol 14 (3) ◽  
Author(s):  
Giovanni Molica Bisci ◽  
Bruno Antonio Pansera
Keyword(s):  
Critical Point ◽  
Sobolev Spaces ◽  
Weak Solutions ◽  
Variational Formulation ◽  
Fractional Laplacian ◽  
Dirichlet Boundary ◽  
Fractional Sobolev Spaces ◽  
Fractional Equations ◽  
Critical Point Result

AbstractThis article concerns a class of nonlocal fractional Laplacian problems depending of three real parameters. More precisely, by using an appropriate analytical context on fractional Sobolev spaces due to Servadei and Valdinoci (in order to correctly encode the Dirichlet boundary datum in the variational formulation of our problem) we establish the existence of three weak solutions for fractional equations via a recent abstract critical point result for differentiable and parametric functionals recently proved by Ricceri.

scholarly journals One solution for nonlocal fourth order equations

2021 ◽  
Vol 40 ◽  
pp. 1-13
Author(s):  
Ghasem A. Afrouzi ◽  
David Barilla ◽  
Giuseppe Caristi ◽  
Shahin Moradi
Keyword(s):  
Weak Solution ◽  
Boundary Value Problem ◽  
Critical Point ◽  
Fourth Order ◽  
Boundary Value ◽  
Kirchhoff Type ◽  
Fourth Order Equations ◽  
Critical Point Result

A critical point result for differentiable functionals is exploited in order to prove that a suitable class of fourth-order boundary value problem of Kirchhoff-type possesses at least one weak solution under an asymptotical behavior of the nonlinear datum at zero. Some examples to illustrate the results are given.

scholarly journals EXISTENCE OF TWO NON-TRIVIAL SOLUTIONS FOR A CLASS OF QUASILINEAR ELLIPTIC VARIATIONAL SYSTEMS ON STRIP-LIKE DOMAINS

2005 ◽  
Vol 48 (2) ◽  
pp. 465-477 ◽  
Author(s):  
Alexandru Kristály
Keyword(s):  
Critical Point ◽  
Elliptic System ◽  
Open Interval ◽  
Growth Conditions ◽  
Quasilinear Elliptic System ◽  
Multiplicity Of Solutions ◽  
Principle Of Symmetric Criticality ◽  
Critical Point Result ◽  
Quasilinear Elliptic ◽  
Variational Systems

AbstractIn this paper we study the multiplicity of solutions of the quasilinear elliptic system\begin{equation} \left. \begin{aligned} -\Delta_pu\amp=\lambda F_u(x,u,v)\amp\amp\text{in }\varOmega, \\ -\Delta_qv\amp=\lambda F_v(x,u,v)\amp\amp\text{in }\varOmega, \\ u=v\amp=0\amp\amp\text{on }\partial\varOmega, \end{aligned} \right\} \end{equation} \tag{S$_\lambda$}where $\varOmega$ is a strip-like domain and $\lambda>0$ is a parameter. Under some growth conditions on $F$, we guarantee the existence of an open interval $\varLambda\subset(0,\infty)$ such that for every $\lambda\in\varLambda$, the system (S$_\lambda$) has at least two distinct, non-trivial solutions. The proof is based on an abstract critical-point result of Ricceri and on the principle of symmetric criticality.

THREE NON-ZERO SOLUTIONS FOR ELLIPTIC NEUMANN PROBLEMS

2011 ◽  
Vol 09 (04) ◽  
pp. 383-394 ◽  
Author(s):  
GIUSEPPINA D'AGUÌ ◽  
GIOVANNI MOLICA BISCI
Keyword(s):  
Critical Point ◽  
Neumann Problem ◽  
Weak Solutions ◽  
Open Interval ◽  
Multiplicity Result ◽  
Neumann Problems ◽  
Critical Point Result

In this note we obtain a multiplicity result for an eigenvalue Neumann problem. Precisely, a recent critical point result for differentiable functionals is exploited, in order to prove the existence of a determined open interval of positive eigenvalues for which the problem admits at least three non-zero weak solutions.

The Critical Point Drying Method Applied to Scanning Electron Microscopy of L-929 Cells

1970 ◽  
Vol 28 ◽  
pp. 278-279
Author(s):  
Charles TurnbiLL ◽  
Delbert E. Philpott
Keyword(s):  
Electron Microscopy ◽  
Carbon Dioxide ◽  
Surface Tension ◽  
Critical Point ◽  
Freeze Drying ◽  
Attractive Alternative ◽  
Crystal Formation ◽  
Critical Point Drying ◽  
Time Required ◽  
Scanning Electron

The advent of the scanning electron microscope (SCEM) has renewed interest in preparing specimens by avoiding the forces of surface tension. The present method of freeze drying by Boyde and Barger (1969) and Small and Marszalek (1969) does prevent surface tension but ice crystal formation and time required for pumping out the specimen to dryness has discouraged us. We believe an attractive alternative to freeze drying is the critical point method originated by Anderson (1951; for electron microscopy. He avoided surface tension effects during drying by first exchanging the specimen water with alcohol, amy L acetate and then with carbon dioxide. He then selected a specific temperature (36.5°C) and pressure (72 Atm.) at which carbon dioxide would pass from the liquid to the gaseous phase without the effect of surface tension This combination of temperature and, pressure is known as the "critical point" of the Liquid.

SEM Cold Stage Techniques for the Observation of Vegetative and Floral Apices of Oat (Avena sativa L.) Plants

1977 ◽  
Vol 35 ◽  
pp. 590-591
Author(s):  
B. K. Kirchoff ◽  
L.F. Allard ◽  
W.C. Bigelow
Keyword(s):  
Critical Point ◽  
Avena Sativa ◽  
Substantial Improvement ◽  
Fresh Tissue ◽  
Cold Stage ◽  
Critical Point Drying ◽  
Almost All ◽  
Cell Collapse ◽  
Conductive Paint ◽  
Carbon Based

In attempting to use the SEM to investigate the transition from the vegetative to the floral state in oat (Avena sativa L.) it was discovered that the procedures of fixation and critical point drying (CPD), and fresh tissue examination of the specimens gave unsatisfactory results. In most cases, by using these techniques, cells of the tissue were collapsed or otherwise visibly distorted. Figure 1 shows the results of fixation with 4.5% formaldehyde-gluteraldehyde followed by CPD. Almost all cellular detail has been obscured by the resulting shrinkage distortions. The larger cracks seen on the left of the picture may be due to dissection damage, rather than CPD. The results of observation of fresh tissue are seen in Fig. 2. Although there is a substantial improvement over CPD, some cell collapse still occurs.Due to these difficulties, it was decided to experiment with cold stage techniques. The specimens to be observed were dissected out and attached to the sample stub using a carbon based conductive paint in acetone.

The Effects of Drying Techniques on Clay-Rich Soil Texture

1974 ◽  
Vol 32 ◽  
pp. 466-467
Author(s):  
T. G. Naymik
Keyword(s):  
Critical Point ◽  
Liquid Nitrogen ◽  
Liquid Nitrogen Temperature ◽  
Drying Methods ◽  
Air Drying ◽  
Freeze Dried ◽  
Critical Point Drying ◽  
Set Up ◽  
The Relationship ◽  
Quartz Grains

Three techniques were incorporated for drying clay-rich specimens: air-drying, freeze-drying and critical point drying. In air-drying, the specimens were set out for several days to dry or were placed in an oven (80°F) for several hours. The freeze-dried specimens were frozen by immersion in liquid nitrogen or in isopentane at near liquid nitrogen temperature and then were immediately placed in the freeze-dry vacuum chamber. The critical point specimens were molded in agar immediately after sampling. When the agar had set up the dehydration series, water-alcohol-amyl acetate-CO2 was carried out. The objectives were to compare the fabric plasmas (clays and precipitates), fabricskeletons (quartz grains) and the relationship between them for each drying technique. The three drying methods are not only applicable to the study of treated soils, but can be incorporated into all SEM clay soil studies.

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