Search results for "Critical points"

showing 10 items of 44 documents

On the existence and multiplicity of solutions for Dirichlet's problem for fractional differential equations

2016

In this paper, by using variational methods and critical point theorems, we prove the existence and multiplicity of solutions for boundary value problem for fractional order differential equations where Riemann-Liouville fractional derivatives and Caputo fractional derivatives are used. Our results extend the second order boundary value problem to the non integer case. Moreover, some conditions to determinate nonnegative solutions are presented and examples are given to illustrate our results.

Applied Mathematics010102 general mathematicsMathematical analysisMultiplicity (mathematics)01 natural sciencesDirichlet distribution010101 applied mathematicssymbols.namesakeSettore MAT/05 - Analisi MatematicasymbolsApplied mathematics0101 mathematicsFractional differentialAnalysisfractional differential equations critical points theorem variational methods multiple solutionsMathematics
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Characterization of the pressure induced Ringwoodite toMg-perovskite and Mg-wüstite phase transition by Catastrophe Theory

2010

Bader’s topological analysis Catastrophe Theory ab initio critical points
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The pressure-induced ringwoodite to Mg-perovskite and periclase post-spinel phase transition: a Bader’s topological analysis of the ab initio electro…

2011

In order to characterize the pressure-induced decomposition of ringwoodite (c-Mg2SiO4), the topological analysis of the electron density q(r), based upon the theory of atoms in molecules (AIM) developed by Bader in the framework of the catastrophe theory, has been performed. Calculations have been carried out by means of the ab initio CRYSTAL09 code at the HF/DFT level, using Hamiltonians based on the Becke- LYP scheme containing hybrid Hartree– Fock/density functional exchange–correlation terms. The equation of state at 0 K has been constructed for the three phases involved in the post-spinel phase transition (ringwoodite -> Mg-perovskite + periclase) occurring at the transition zone–lower…

Bader’s topological analysisElectron densityEquation of statePhase transitionRingwoodite Post-spinel phase transition Bader’s topological analysis Ab initio Catastrophe theory Critical pointsChemistryCatastrophe theoryAtoms in moleculesRingwooditeAb initioCritical pointsHartreeengineering.materialTopologyRingwoodite; Post-spinel phase transition; Bader’s topological analysis; Ab initio; Catastrophe theory; Critical pointsPost-spinel phase transitionRingwooditeGeochemistry and PetrologyBader’s topological analysiAb initioengineeringGeneral Materials SciencePerovskite (structure)
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Oscillatory integrals and fractal dimension

2021

Theory of singularities has been closely related with the study of oscillatory integrals. More precisely, the study of critical points is closely related to the study of asymptotic of oscillatory integrals. In our work we investigate the fractal properties of a geometrical representation of oscillatory integrals. We are motivated by a geometrical representation of Fresnel integrals by a spiral called the clothoid, and the idea to produce a classification of singularities using fractal dimension. Fresnel integrals are a well known class of oscillatory integrals. We consider oscillatory integral $$ I(\tau)=\int_{; ; \mathbb{; ; R}; ; ^n}; ; e^{; ; i\tau f(x)}; ; \phi(x) dx, $$ for large value…

Box dimensionGeneral Mathematics010102 general mathematicsMathematical analysisPhase (waves)Resolution of singularitiesOscillatory integral ; Box dimension ; Minkowski content ; Critical points ; Newton diagramCritical points01 natural sciencesFractal dimensionCritical point (mathematics)Oscillatory integralAmplitudeDimension (vector space)Mathematics - Classical Analysis and ODEsMinkowski contentClassical Analysis and ODEs (math.CA)FOS: Mathematics0101 mathematicsMinkowski contentOscillatory integralNewton diagram[MATH]Mathematics [math]fractal dimension; box dimension; oscillatory integrals; theory of singularitiesMathematics
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Calibrations and isoperimetric profiles

2007

We equip many noncompact nonsimply connected surfaces with smooth Riemannian metrics whose isoperimetric profile is smooth, a highly nongeneric property. The computation of the profile is based on a calibration argument, a rearrangement argument, the Bol-Fiala curvature dependent inequality, together with new results on the profile of surfaces of revolution and some hardware know-how.

Calibration Riemann manifold Critical points Surfaces of revolution Radius of curvature Mathematical surfaces Mathematical constants DuetsSettore MAT/03 - Geometria
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A Mountain Pass Theorem for a Suitable Class of Functions

2009

Class (set theory)geographyPure mathematicsgeography.geographical_feature_categorycritical pointsGeneral Mathematicsthree solutions58E30two-point boundary value problemPalais-Smale conditionmountain pass34B1558E05A mountain pass theoremCombinatoricsPalais–Smale compactness conditionSettore MAT/05 - Analisi MatematicaMountain pass theoremMountain pass49J4047J30Mathematics
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Multiple solutions for a discrete boundary value problem involving the p-Laplacian.

2008

Multiple solutions for a discrete boundary value problem involving the p-Laplacian are established. Our approach is based on critical point theory.

Computational MathematicsComputational Theory and MathematicsSettore MAT/05 - Analisi MatematicaModeling and SimulationMathematical analysisFree boundary problemp-LaplacianBoundary value problemMixed boundary conditionElliptic boundary value problemCritical point (mathematics)Discrete boundary value problem multiple solutions p-Laplacian critical points theoryMathematics
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Existence and multiplicity of periodic solutions for second order Hamiltonian systems depending on a parameter

2013

The existence of at least one nontrivial periodic solution for a class of second order Hamiltonian systems depending on a parameter is obtained, under an algebraic condition on the nonlinearity G and without requiring any asymptotic behavior neither at zero nor at infinity. The existence is still deduced in the particular case when G is subquadratic at zero. Finally, two multiplicity results are proved if G, in addition, is required to fulfill some different Ambrosetti-Rabinowitz type superquadratic conditions at infinity. The approach is fully variational. © Heldermann Verlag.

Critical points Periodic solutions Second order hamiltonian systemsPeriodic solutionsPeriodic solutionCritical pointsSecond order hamiltonian systemsCritical point
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Multiple solutions for a Sturm-Liouville problem with mixed boundary conditions

2010

Critical points mixed boundary value problems multiple solutions
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Minimal unit vector fields

2002

We compute the first variation of the functional that assigns each unit vector field the volume of its image in the unit tangent bundle. It is shown that critical points are exactly those vector fields that determine a minimal immersion. We also find a necessary and sufficient condition that a vector field, defined in an open manifold, must fulfill to be minimal, and obtain a simpler equivalent condition when the vector field is Killing. The condition is fulfilled, in particular, by the characteristic vector field of a Sasakian manifold and by Hopf vector fields on spheres.

Curl (mathematics)Killing vector fieldsSolenoidal vector fieldVector operatorcritical pointsGeneral Mathematicsminimal vector fieldsMathematical analysis53C4253C20Hopf vector fields53C25Sasakian manifoldsKilling vector fieldUnit vectorFundamental vector fieldMathematics::Differential GeometryVolume of vector fieldsComplex lamellar vector fieldVector potentialMathematicsTohoku Mathematical Journal
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