Search results for "Double phase problem"

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Positive solutions for singular double phase problems

2021

Abstract We study the existence of positive solutions for a class of double phase Dirichlet equations which have the combined effects of a singular term and of a parametric superlinear term. The differential operator of the equation is the sum of a p-Laplacian and of a weighted q-Laplacian ( q p ) with discontinuous weight. Using the Nehari method, we show that for all small values of the parameter λ > 0 , the equation has at least two positive solutions.

Class (set theory)Double phase problemNehari manifold01 natural sciencesDirichlet distributionsymbols.namesakeMathematics - Analysis of PDEsSettore MAT/05 - Analisi MatematicaFOS: MathematicsApplied mathematics0101 mathematics35J60 35D05Positive solutionsParametric statisticsMathematicsApplied Mathematics010102 general mathematicsSingular termSingular termMathematics::Spectral TheoryDifferential operatorTerm (time)010101 applied mathematicsDouble phaseDiscontinuous weightsymbolsAnalysisAnalysis of PDEs (math.AP)
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Positive solutions for singular (p, 2)-equations

2019

We consider a nonlinear nonparametric Dirichlet problem driven by the sum of a p-Laplacian and of a Laplacian (a (p, 2)-equation) and a reaction which involves a singular term and a $$(p-1)$$ -superlinear perturbation. Using variational tools and suitable truncation and comparison techniques, we show that the problem has two positive smooth solutions.

Dirichlet problemApplied MathematicsGeneral Mathematics010102 general mathematicsNonparametric statisticsSingular termGeneral Physics and AstronomyPerturbation (astronomy)Mathematics::Spectral Theory01 natural sciences010101 applied mathematicsNonlinear systemSettore MAT/05 - Analisi MatematicaSingular term Superlinear perturbation Positive solution Nonlinear regularity Truncation Maximum principle Double phase problemApplied mathematics0101 mathematicsLaplace operatorMathematicsZeitschrift für angewandte Mathematik und Physik
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