Search results for "multiple solutions."

showing 10 items of 12 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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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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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 eigenvalue Dirichlet problem involving the p-Laplacian with discontinuous nonlinearities

2005

AbstractA multiplicity result for an eigenvalue Dirichlet problem involving the p-Laplacian with discontinuous nonlinearities is obtained. The proof is based on a three critical points theorem for nondifferentiable functionals.

Dirichlet problemDiscontinuous nonlinearitiesApplied MathematicsMathematical analysisp-LaplacianMultiple solutionsMathematics::Optimization and ControlDirichlet's energyMathematics::Spectral TheoryEigenvalue Dirichlet problemCritical points of nonsmooth functionsNonlinear systemsymbols.namesakeDirichlet eigenvalueDirichlet's principleRayleigh–Faber–Krahn inequalitysymbolsp-LaplacianEigenvalues and eigenvectorsAnalysisMathematicsJournal of Mathematical Analysis and Applications
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Multiple solutions for a Dirichlet problem with p-Laplacian and set-valued nonlinearity

2008

AbstractThe existence of a negative solution, of a positive solution, and of a sign-changing solution to a Dirichlet eigenvalue problem with p-Laplacian and multi-valued nonlinearity is investigated via sub- and supersolution methods as well as variational techniques for nonsmooth functions.

Dirichlet problemGeneral MathematicsMathematical analysisNull (mathematics)Multiple solutions Dirichlet problem p-Laplacian set-valued nonlinearitySet (abstract data type)symbols.namesakeGeneralized gradientNonlinear systemDirichlet eigenvalueSettore MAT/05 - Analisi MatematicaDirichlet's principlep-LaplaciansymbolsMathematics
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Existence of three solutions for a quasilinear two point boundary value problem

2002

In this paper we deal with the existence of at least three classical solutions for the following ordinary Dirichlet problem:¶¶ $ \left\{\begin{array}{ll} u'' + \lambda h(u')f(t,\:u) = 0\\ u(0) = u(1) = 0.\\\end{array}\right.\ $ ¶¶Our main tool is a recent three critical points theorem of B. Ricceri ([10]).

Dirichlet problemPoint boundaryPure mathematicsMultiple solutions critical point theoryGeneral MathematicsMathematical analysisLambdaValue (mathematics)MathematicsArchiv der Mathematik
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Existence of non-zero solutions for a Dirichlet problem driven by (p(x),q(x)-Laplacian

2021

The paper focuses on a Dirichlet problem driven by the (Formula presented.) -Laplacian. The existence of at least two non-zero solutions under suitable conditions on the nonlinear term is established. The approach is based on variational methods.

Dirichlet problemPure mathematicsmultiple solutionscritical pointsApplied Mathematics010102 general mathematicsZero (complex analysis)q(x))-LaplacianMathematics::Spectral Theory-Laplacian01 natural sciences(p(x)q(x))-Laplacian critical points multiple solutions Dirichlet problemTerm (time)010101 applied mathematicsNonlinear systemSettore MAT/05 - Analisi Matematica0101 mathematics(p(x)Laplace operatorAnalysisDirichlet problemMathematicsApplicable Analysis
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On Different Type Solutions of Boundary Value Problems

2016

We consider boundary value problems of the type x'' = f(t, x, x'), (∗) x(a) = A, x(b) = B. A solution ξ(t) of the above BVP is said to be of type i if a solution y(t) of the respective equation of variations y'' = fx(t, ξ(t), ξ' (t))y + fx' (t, ξ(t), ξ' (t))y' , y(a) = 0, y' (a) = 1, has exactly i zeros in the interval (a, b) and y(b) 6= 0. Suppose there exist two solutions x1(t) and x2(t) of the BVP. We study properties of the set S of all solutions x(t) of the equation (∗) such that x(a) = A, x'1(a) ≤ x' (a) ≤ x'2(a) provided that solutions extend to the interval [a, b].

Discrete mathematicsmultiple solutionsexistence010103 numerical & computational mathematicsType (model theory)01 natural sciences010101 applied mathematicsSet (abstract data type)Modeling and Simulationboundary value problemQA1-939Interval (graph theory)Boundary value problem0101 mathematicsAnalysisMathematicsMathematicsMathematical Modelling and Analysis
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Critical points for nondifferentiable functions in presence of splitting

2006

A classical critical point theorem in presence of splitting established by Brézis-Nirenberg is extended to functionals which are the sum of a locally Lipschitz continuous term and of a convex, proper, lower semicontinuous function. The obtained result is then exploited to prove a multiplicity theorem for a family of elliptic variational-hemivariational eigenvalue problems. © 2005 Elsevier Inc. All rights reserved.

Mathematics::Functional AnalysisPure mathematicsnon-smooth functionNonsmooth functionssplittingApplied MathematicsMathematical analysisMultiple solutionsMultiple solutionMathematics::Analysis of PDEsRegular polygoncritical point; non-smooth function; splittingcritical pointMultiplicity (mathematics)Critical pointsNonsmooth functionElliptic variational-hemivariational eigenvalue problemLipschitz continuityCritical point (mathematics)Elliptic variational–hemivariational eigenvalue problemsSplittingsEigenvalues and eigenvectorsAnalysisMathematics
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Periodic solutions for a class of second-order Hamiltonian systems

2005

Multiplicity results for an eigenvalue second-order Hamiltonian system are investigated. Using suitable critical points arguments, the existence of an exactly determined open interval of positive eigenvalues for which the system admits at least three distinct periodic solutions is established. Moreover, when the energy functional related to the Hamiltonian system is not coercive, an existence result of two distinct periodic solutions is given.© 2005 Texas State University - San Marcos.

Second order Hamiltonian systemPeriodic solutioncritical pointslcsh:MathematicsMultiple solutioneigenvalue problemperiodic solutionslcsh:QA1-939Second order Hamiltonian systemsAnalysisCritical pointmultiple solutions.Electronic Journal of Differential Equations
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