Search results for "variational methods"

showing 10 items of 20 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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A double mean field equation related to a curvature prescription problem

2019

We study a double mean field-type PDE related to a prescribed curvature problem on compacts surfaces with boundary. We provide a general blow-up analysis, then a Moser-Trudinger inequality, which gives energy-minimizing solutions for some range of parameters. Finally, we provide existence of min-max solutions for a wider range of parameters, which is dense in the plane if $��$ is not simply connected.

Blow–up analysiPlane (geometry)Applied Mathematics010102 general mathematicsMathematics::Analysis of PDEs35J20 58J32Boundary (topology)Unit normal vectorCurvature01 natural sciencesConformal metric010101 applied mathematicsMathematics - Analysis of PDEsVariational methodsMean field equationSimply connected spaceFOS: Mathematics0101 mathematicsPrescribed curvature problemAnalysisMathematical physicsMathematicsAnalysis of PDEs (math.AP)
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Infinitely many solutions for a perturbed p-Laplacian boundary value problem with impulsive effects

2017

In this paper, we deal with the existence of weak solutions for a perturbed p-Laplacian boundary value problem with impulsive effects. More precisely, the existence of an exactly determined open interval of positive parameters for which the problem admits infinitely many weak solutions is established. Our proofs are based on variational methods.

Control and OptimizationApplied MathematicsPerturbed p-Laplacian boundary value problemCritical point theory; Impulsive effects; Infinitely many solutions; Perturbed p-Laplacian boundary value problem; Variational methods; Analysis; Geometry and Topology; Control and Optimization; Applied MathematicsVariational methodAnalysiImpulsive effectsInfinitely many solutionsImpulsive effectVariational methodsCritical point theoryInfinitely many solutionGeometry and TopologyAnalysis
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Triple solutions for nonlinear elliptic problems driven by a non-homogeneous operator

2020

Abstract Some multiplicity results for a parametric nonlinear Dirichlet problem involving a nonhomogeneous differential operator of p -Laplacian type are given. Via variational methods, the article furnishes new contributions and completes some previous results obtained for problems considering other types of differential operators and/or nonlinear terms satisfying different asymptotic conditions.

Dirichlet problemApplied Mathematics010102 general mathematicsMultiple solutionsp-LaplacianMultiple solutionType (model theory)Differential operator01 natural sciencesCritical point010101 applied mathematicsNonlinear systemOperator (computer programming)Critical point; Multiple solutions; Nonlinear elliptic problem; p-Laplacian; Variational methodsVariational methodsSettore MAT/05 - Analisi MatematicaNon homogeneousApplied mathematicsNonlinear elliptic problem0101 mathematicsLaplace operatorAnalysisMathematicsParametric statistics
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CLEAR: Covariant LEAst-Square Refitting with Applications to Image Restoration

2017

International audience; In this paper, we propose a new framework to remove parts of the systematic errors affecting popular restoration algorithms, with a special focus for image processing tasks. Generalizing ideas that emerged for $\ell_1$ regularization, we develop an approach re-fitting the results of standard methods towards the input data. Total variation regularizations and non-local means are special cases of interest. We identify important covariant information that should be preserved by the re-fitting method, and emphasize the importance of preserving the Jacobian (w.r.t. the observed signal) of the original estimator. Then, we provide an approach that has a ``twicing'' flavor a…

FOS: Computer and information sciencesInverse problemsMathematical optimization[ INFO.INFO-TS ] Computer Science [cs]/Signal and Image ProcessingComputer Vision and Pattern Recognition (cs.CV)General MathematicsComputer Science - Computer Vision and Pattern RecognitionMachine Learning (stat.ML)Mathematics - Statistics TheoryImage processingStatistics Theory (math.ST)02 engineering and technologyDebiasing[ INFO.INFO-CV ] Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV]01 natural sciencesRegularization (mathematics)Boosting010104 statistics & probabilitysymbols.namesake[INFO.INFO-TS]Computer Science [cs]/Signal and Image Processing[STAT.ML]Statistics [stat]/Machine Learning [stat.ML]Variational methods[MATH.MATH-ST]Mathematics [math]/Statistics [math.ST]Statistics - Machine LearningRefittingMSC: 49N45 65K10 68U10[ INFO.INFO-TI ] Computer Science [cs]/Image ProcessingFOS: Mathematics0202 electrical engineering electronic engineering information engineeringCovariant transformation[ MATH.MATH-ST ] Mathematics [math]/Statistics [math.ST]0101 mathematicsImage restoration[ STAT.ML ] Statistics [stat]/Machine Learning [stat.ML]MathematicsApplied Mathematics[INFO.INFO-CV]Computer Science [cs]/Computer Vision and Pattern Recognition [cs.CV]EstimatorInverse problem[INFO.INFO-TI]Computer Science [cs]/Image Processing [eess.IV]Jacobian matrix and determinantsymbolsTwicing020201 artificial intelligence & image processingAffine transformationAlgorithm
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An Existence Result for Fractional Kirchhoff-Type Equations

2016

The aim of this paper is to study a class of nonlocal fractional Laplacian equations of Kirchhoff-type. More precisely, by using an appropriate analytical context on fractional Sobolev spaces, we establish the existence of one non-trivial weak solution for nonlocal fractional problems exploiting suitable variational methods.

Kirchhoff typeApplied MathematicsFractional equations010102 general mathematicsMathematical analysisvariational methodsVariational methodAnalysiCritical point result01 natural sciencesFractional equationsFractional equationFractional calculus010101 applied mathematicscritical point resultsSimultaneous equations0101 mathematicsFractional equations variational methods critical point resultsAnalysisMathematicsZeitschrift für Analysis und ihre Anwendungen
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Multiplicity results for Sturm-Liouville boundary value problems

2009

Multiplicity results for Sturm-Liouville boundary value problems are obtained. Proofs are based on variational methods.

Partial differential equationSturm-Liouville problem variational methodsApplied MathematicsNumerical analysisMultiplicity resultsMathematical analysisSturm–Liouville theoryMixed boundary conditionMathematics::Spectral TheoryMathematical proofCritical point (mathematics)Computational MathematicsSettore MAT/05 - Analisi MatematicaBoundary value problemMathematics
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Infinitely many weak solutions for a mixed boundary value system with (p_1,…,p_m)-Laplacian

2014

The aim of this paper is to prove the existence of infinitely many weak solu- tions for a mixed boundary value system with (p1, . . . , pm)-Laplacian. The approach is based on variational methods.

Pure mathematicscritical pointsinfinitely many solutionsApplied MathematicsMathematical analysisvariational methodsBoundary valuesCritical points variational methods infinitely many solutions p-Laplacian.$p$-laplacianSettore MAT/05 - Analisi MatematicaQA1-939Laplace operatorMathematicsMathematics
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Existence and multiplicity results for semilinear elliptic Dirichlet problems in exterior domains

1995

Pure mathematicslack of emptinesspositive solutionsApplied MathematicsMultiplicity resultsNonlinear elliptic Dirichlet problemsMathematical analysisDirichlet L-functionvariational methodsDirichlet's energyDirichlet distributionExterior domainsDirichlet kernelsymbols.namesakeDirichlet's principlesymbolsExterior domains; lack of emptiness; Nonlinear elliptic Dirichlet problems; positive solutions; variational methodsAnalysisDirichlet seriesMathematics
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Ordinary (p_1,...,p_m)-Laplacian system with mixed boundary value

2016

In this paper we prove the existence of multiple weak solutions for an ordinary mixed boundary value system with (p_1,...,p_m)-Laplacian by using recent results of critical points.

Settore MAT/05 - Analisi MatematicaMultiple critical points variational methods p-Laplacian boundary value problem
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