Search results for "General Dirichlet series"

showing 4 items of 4 documents

Dirichlet Forms, Poincaré Inequalities, and the Sobolev Spaces of Korevaar and Schoen

2004

We answer a question of Jost on the validity of Poincare inequalities for metric space-valued functions in a Dirichlet domain. We also investigate the relationship between Dirichlet domains and the Sobolev-type spaces introduced by Korevaar and Schoen.

Discrete mathematicsDirichlet formMathematics::Analysis of PDEsDirichlet L-functionDirichlet's energyMathematics::Spectral Theorysymbols.namesakeDirichlet kernelDirichlet's principlesymbolsGeneral Dirichlet seriesAnalysisDirichlet seriesMathematicsSobolev spaces for planar domainsPotential Analysis
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Multiplicity of solutions of Dirichlet problems associated with second-order equations in ℝ2

2009

AbstractWe study the existence of multiple solutions for a two-point boundary-value problem associated with a planar system of second-order ordinary differential equations by using a shooting technique. We consider asymptotically linear nonlinearities satisfying suitable sign conditions. Multiplicity is ensured by assumptions involving the Morse indices of the linearizations at zero and at infinity.

General MathematicsDirichlet L-functionasymptotically linear multiplicity second order planar systems Morse indexDirichlet's energyDirichlet integralsymbols.namesakeDirichlet eigenvalueSettore MAT/05 - Analisi MatematicaDirichlet's principleOrdinary differential equationDirichlet boundary conditionsymbolsApplied mathematicsGeneral Dirichlet seriesMathematics
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Multiplicity theorems for the Dirichlet problem involving the p-Laplacian

2003

Multiplicity theorems for the Dirichlet problem involving the p-Laplacian were proved using variational approach. It was shown that there existed an open interval and a positive real number, and each problem admits at least three weak solutions. Results on the existence of at least three weak solutions for the Dirichlet problems were established.

Pure mathematicsApplied Mathematicsp-LaplacianMathematical analysisMultiple solutionDirichlet L-functionAnalysiDirichlet's energyMathematics::Spectral TheoryCritical pointDirichlet kernelsymbols.namesakeDirichlet eigenvalueDirichlet's principleDirichlet boundary conditionsymbolsMathematics (all)General Dirichlet seriesAnalysisDirichlet seriesDirichlet problemMathematicsNonlinear Analysis: Theory, Methods & Applications
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Banach spaces of general Dirichlet series

2018

Abstract We study when the spaces of general Dirichlet series bounded on a half plane are Banach spaces, and show that some of those classes are isometrically isomorphic between themselves. In a precise way, let { λ n } be a strictly increasing sequence of positive real numbers such that lim n → ∞ ⁡ λ n = ∞ . We denote by H ∞ ( λ n ) the complex normed space of all Dirichlet series D ( s ) = ∑ n b n λ n − s , which are convergent and bounded on the half plane [ Re s > 0 ] , endowed with the norm ‖ D ‖ ∞ = sup Re s > 0 ⁡ | D ( s ) | . If (⁎) there exists q > 0 such that inf n ⁡ ( λ n + 1 q − λ n q ) > 0 , then H ∞ ( λ n ) is a Banach space. Further, if there exists a strictly increasing sequ…

SequenceApplied Mathematics010102 general mathematicsBanach space01 natural sciences010101 applied mathematicsCombinatoricssymbols.namesakeBounded functionsymbolsLinear independence0101 mathematicsPositive real numbersGeneral Dirichlet seriesAnalysisDirichlet seriesMathematicsNormed vector spaceJournal of Mathematical Analysis and Applications
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