Search results for "Variable exponent"

showing 8 items of 8 documents

Three solutions to mixed boundary value problem driven by p(z)-Laplace operator

2021

We prove the existence of at least three weak solutions to a mixed Dirichlet–Neumann boundary value problem for equations driven by the p(z)-Laplace operator in the principal part. Our approach is variational and use three critical points theorems.

Dirichlet–Neumann boundary value problemSettore MAT/05 - Analisi MatematicaGeneral MathematicsMathematical analysisp(z)-Laplace operatorBoundary value problemvariable exponent Sobolev spaceLaplace operatorMathematics
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On ( p ( x ),  q ( x ))‐Laplace equations in ℝN without Ambrosetti‐Rabinowitz condition

2021

In the present work, we consider a (p(x), q(x))-elliptic equation describing the behavior of a double-phase anisotropic problem which has relevance in electrorheological fluid applications. The analysis leads to the existence of weak (nonnegative) solutions in the special case of potential terms with critical frequency and a superlinear reaction term. In order to prove the existence result, we combine critical point theory of mountain pass type with related topological and variational methods. Basically, the approach is variational, but we do not impose any Ambrosetti-Rabinowitz type condition for the superlinearity of the reaction. More specifically, we apply the Euler-Lagrange functional …

Elliptic curvevariable exponentLaplace transformVariable exponentCritical frequencyelliptic equationGeneral MathematicsMathematical analysisGeneral Engineering(p(x) q(x))-Laplace operatorcritical frequencyMathematicsMathematical Methods in the Applied Sciences
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Weak solutions to Dirichlet boundary value problem driven by p(x)-Laplacian-like operator

2017

We prove the existence of weak solutions to the Dirichlet boundary value problem for equations involving the $p(x)$-Laplacian-like operator in the principal part, with reaction term satisfying a sub-critical growth condition. We establish the existence of at least one nontrivial weak solution and three weak solutions, by using variational methods and critical point theory.

Pure mathematicsApplied MathematicsOperator (physics)010102 general mathematicsdirichlet boundary value problem01 natural sciencesDirichlet distribution010101 applied mathematicssymbols.namesakeSettore MAT/05 - Analisi MatematicaP(x)-Laplacian-like operatorQA1-939symbolsvariable exponent sobolev spaceBoundary value problem0101 mathematics$p(x)$-laplacian-like operatorLaplace operatorMathematicsMathematicsElectronic Journal of Qualitative Theory of Differential Equations
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Multiple solutions for a Neumann-type differential inclusion problem involving the p(.)-Laplacian

2012

Using a multiple critical points theorem for locally Lipschitz continuous functionals, we establish the existence of at least three distinct solutions for a Neumann-type differential inclusion problem involving the $p(\cdot)$-Laplacian.

Pure mathematicsApplied Mathematicsthree-critical-points theoremdifferential inclusion problemType (model theory)Lipschitz continuityDifferential inclusionCritical points of locally Lipschitz continuous functionalcritical points of locally Lipschitz continuous functionalsp-LaplacianDiscrete Mathematics and Combinatoricsp(x)-Laplacian; variable exponent Sobolev space; critical points of locally Lipschitz continuous functionals; differential inclusion problem; three-critical-points theoremp(x)-Laplacianvariable exponent Sobolev spaceAnalysisMathematics
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Riesz and Wolff potentials and elliptic equations in variable exponent weak Lebesgue spaces

2015

Submitted by Alexandre Almeida (jaralmeida@ua.pt) on 2015-11-12T11:41:07Z No. of bitstreams: 1 RieszWolff_RIA.pdf: 159825 bytes, checksum: d99abdf3c874f47195619a31ff5c12c7 (MD5) Approved for entry into archive by Bella Nolasco(bellanolasco@ua.pt) on 2015-11-17T12:18:41Z (GMT) No. of bitstreams: 1 RieszWolff_RIA.pdf: 159825 bytes, checksum: d99abdf3c874f47195619a31ff5c12c7 (MD5) Made available in DSpace on 2015-11-17T12:18:41Z (GMT). No. of bitstreams: 1 RieszWolff_RIA.pdf: 159825 bytes, checksum: d99abdf3c874f47195619a31ff5c12c7 (MD5) Previous issue date: 2015-04

Pure mathematicsWolff potentialScale (ratio)Weak Lebesgue spaceVariable exponentMathematics::Classical Analysis and ODEsLebesgue's number lemmaNon-standard growth conditionIntegrability of solutionssymbols.namesakeMathematics - Analysis of PDEsReal interpolationFOS: MathematicsLp spaceMathematicsLaplace's equationMathematics::Functional AnalysisVariable exponentIntegrability estimatesRiesz potentialApplied MathematicsMathematical analysisFunctional Analysis (math.FA)Mathematics - Functional AnalysissymbolsRiesz potential47H99 (Primary) 46B70 46E30 35J60 31C45 (Secondary)Analysis of PDEs (math.AP)
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One-dimensional nonlinear boundary value problems with variable exponent

2018

In this paper, a class of nonlinear differential boundary value problems with variable exponent is investigated. The existence of at least one non-zero solution is established, without assuming on the nonlinear term any condition either at zero or at infinity. The approach is developed within the framework of the Orlicz-Sobolev spaces with variable exponent and it is based on a local minimum theorem for differentiable functions.

Variable exponent Sobolev spacemedia_common.quotation_subject02 engineering and technology01 natural sciences0202 electrical engineering electronic engineering information engineeringDiscrete Mathematics and CombinatoricsBoundary value problemDifferentiable function0101 mathematicsDifferential (infinitesimal)P(x)-LaplacianDiscrete Mathematics and Combinatoricmedia_commonMathematicsDirichlet problemDirichlet problemApplied Mathematics010102 general mathematicsMathematical analysisZero (complex analysis)AnalysiDirichlet problem; P(x)-Laplacian; Variable exponent Sobolev spaces; Analysis; Discrete Mathematics and Combinatorics; Applied MathematicsMixed boundary conditionInfinityNonlinear system020201 artificial intelligence & image processingAnalysis
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Recovering a variable exponent

2021

We consider an inverse problem of recovering the non-linearity in the one dimensional variable exponent $p(x)$-Laplace equation from the Dirichlet-to-Neumann map. The variable exponent can be recovered up to the natural obstruction of rearrangements. The main technique is using the properties of a moment problem after reducing the inverse problem to determining a function from its $L^p$-norms.

non-standard growthvariable exponentelliptic equationGeneral Mathematicsquasilinear equationinversio-ongelmatCalderón's problemMathematics - Analysis of PDEsapproximation by polynomialsFOS: Mathematics34A55 (Primary) 41A10 34B15 28A25 (Secondary)inverse problemapproksimointiMüntz-Szász theoremdifferentiaaliyhtälötAnalysis of PDEs (math.AP)Documenta Mathematica
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Constant sign and nodal solutions for parametric anisotropic $(p, 2)$-equations

2021

We consider an anisotropic ▫$(p, 2)$▫-equation, with a parametric and superlinear reaction term.Weshow that for all small values of the parameter the problem has at least five nontrivial smooth solutions, four with constant sign and the fifth nodal (sign-changing). The proofs use tools from critical point theory, truncation and comparison techniques, and critical groups. Spletna objava: 9. 9. 2021. Abstract. Bibliografija: str. 1076.

udc:517.9electrorheological fluidsElectrorheological fluidMaximum principleMathematics - Analysis of PDEsSettore MAT/05 - Analisi MatematicaFOS: Mathematicsconstant sign and nodal solutionsAnisotropyanisotropic operators regularity theory maximum principle constant sign and nodal solutions critical groups variable exponent electrorheological fluidsParametric statisticsMathematicsvariable exponentVariable exponentApplied MathematicsMathematical analysisudc:517.956.2regularity theoryAnisotropic operatorsanisotropic operatorsTerm (time)Primary: 35J20 35J60 35J92 Secondary: 47J15 58E05maximum principleConstant (mathematics)critical groupsAnalysisAnalysis of PDEs (math.AP)Sign (mathematics)
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