Search results for "Orlicz-Sobolev spaces"

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Elliptic problems with convection terms in Orlicz spaces

2021

Abstract The existence of a solution to a Dirichlet problem, for a class of nonlinear elliptic equations, with a convection term, is established. The main novelties of the paper stand on general growth conditions on the gradient variable, and on minimal assumptions on Ω. The approach is based on the method of sub and supersolutions. The solution is a zero of an auxiliary pseudomonotone operator build via truncation techniques. We present also some examples in which we highlight the generality of our growth conditions.

Dirichlet problemGradient dependenceClass (set theory)Truncation methodsTruncationApplied Mathematics010102 general mathematicsZero (complex analysis)Orlicz-Sobolev spacesNonlinear elliptic equationsTerm (logic)01 natural sciences010101 applied mathematicsNonlinear systemOperator (computer programming)Subsolution and supersolutionSettore MAT/05 - Analisi MatematicaApplied mathematics0101 mathematicsAnalysisMathematicsVariable (mathematics)Journal of Mathematical Analysis and Applications
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Multiple solutions for parametric double phase Dirichlet problems

2020

We consider a parametric double phase Dirichlet problem. Using variational tools together with suitable truncation and comparison techniques, we show that for all parametric values [Formula: see text] the problem has at least three nontrivial solutions, two of which have constant sign. Also, we identify the critical parameter [Formula: see text] precisely in terms of the spectrum of the [Formula: see text]-Laplacian.

Dirichlet problemlocal minimizersTruncationApplied MathematicsGeneral MathematicsMusielak-Orlicz-Sobolev spacesDirichlet distributionsymbols.namesakeDouble phaseSettore MAT/05 - Analisi MatematicaDouble phase integrandsymbolseigenvalues of the q-LaplacianApplied mathematicsSettore MAT/03 - Geometriaunbalanced growthParametric statisticsMathematics
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