Search results for "growth condition"

showing 5 items of 5 documents

On the Sets of Regularity of Solutions for a Class of Degenerate Nonlinear Elliptic Fourth-Order Equations with L1 Data

2007

We establish Holder continuity of generalized solutions of the Dirichlet problem, associated to a degenerate nonlinear fourth-order equation in an open bounded set , with data, on the subsets of where the behavior of weights and of the data is regular enough.

Dirichlet problemPartial differential equationAlgebra and Number TheoryBounded setDifferential equationMathematical analysisDegenerate energy levelsgrowth conditionElliptic equationlcsh:QA299.6-433lcsh:AnalysisRenormalized solutionNonlinear systemSimultaneous equationsOrdinary differential equationAnalysisMathematicsBoundary Value Problems
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Existence and multiplicity of solutions for Dirichlet problems involving nonlinearities with arbitrary growth.

2014

In this article we study the existence and multiplicity of solutions for the Dirichlet problem $$\displaylines{ -\Delta_p u=\lambda f(x,u)+ \mu g(x,u)\quad\hbox{in }\Omega,\cr u=0\quad\hbox{on } \partial \Omega }$$ where $\Omega$ is a bounded domain in $\mathbb{R}^N$, $f,g:\Omega \times \mathbb{R}\to \mathbb{R}$ are Caratheodory functions, and $\lambda,\mu$ are nonnegative parameters. We impose no growth condition at $\infty$ on the nonlinearities f,g. A corollary to our main result improves an existence result recently obtained by Bonanno via a critical point theorem for $C^1$ functionals which do not satisfy the usual sequential weak lower semicontinuity property.

Existence and multiplicity of solutionscritical point theoremSettore MAT/05 - Analisi Matematicalcsh:MathematicsDirichlet problemsgrowth conditionMathematics::Analysis of PDEslcsh:QA1-939Dirichlet problem
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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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Quasilinear elliptic equations with singular quadratic growth terms

2011

In this paper, we deal with positive solutions for singular quasilinear problems whose model is [Formula: see text] where Ω is a bounded open set of ℝN, g ≥ 0 is a function in some Lebesgue space, and γ > 0. We prove both existence and nonexistence of solutions depending on the value of γ and on the size of g.

Quadratic growthnonlinear elliptic equations; natural growth condition; vertical asymptote; measure dataApplied MathematicsGeneral MathematicsMathematical analysisOpen setmeasure dataFunction (mathematics)nonlinear elliptic equationsBounded functionvertical asymptoteStandard probability spacenatural growth conditionAsymptoteValue (mathematics)Mathematics
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Quasihyperbolic boundary condition: Compactness of the inner boundary

2011

We prove that if a metric space satisfies a suitable growth condition in the quasihyperbolic metric and the Gehring–Hayman theorem in the original metric, then the inner boundary of the space is homeomorphic to the Gromov boundary. Thus, the inner boundary is compact. peerReviewed

Gromov boundaryquasihyperbolic metricMathematics::Complex VariablesGeneral Mathematicsgrowth conditionMathematical analysisBoundary (topology)Mixed boundary conditionGromov-reuna30C65Gromov boundaryMetric spaceCompact spaceGromov hyperbolicityGromov-hyperbolisuusMetric (mathematics)Neumann boundary conditionMathematics::Metric Geometrykasvuehtokvasihyperbolinen metriikkaBoundary value problemMathematicsIllinois Journal of Mathematics
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