Search results for " variational method"

showing 10 items of 13 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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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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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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Existence of two positive solutions for anisotropic nonlinear elliptic equations

2021

This paper deals with the existence of nontrivial solutions for a class of nonlinear elliptic equations driven by an anisotropic Laplacian operator. In particular, the existence of two nontrivial solutions is obtained, adapting a two critical point results to a suitable functional framework that involves the anisotropic Sobolev spaces.

Settore MAT/05 - Analisi MatematicaApplied MathematicsAnisotropic problem variational method positive solutions partial differential equationsAnalysis
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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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Two non-zero solutions for Sturm–Liouville equations with mixed boundary conditions

2019

Abstract In this paper, we establish the existence of two non-zero solutions for a mixed boundary value problem with the Sturm–Liouville equation. The approach is based on a recent two critical point theorem.

Sturm–Liouville theoryCritical points01 natural sciencesCritical point (mathematics)Critical pointSturm–Liouville equationVariational methodsBoundary value problem0101 mathematicsBoundary value problem; Critical points; Mixed conditions; Sturm–Liouville equation; Variational methodsBoundary value problemMathematicsApplied Mathematics010102 general mathematicsMathematical analysisGeneral EngineeringVariational methodAnalysiGeneral MedicineMathematics::Spectral Theory010101 applied mathematicsComputational MathematicsMixed conditionGeneral Economics Econometrics and FinanceMixed conditionsAnalysis
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