6533b838fe1ef96bd12a3e2c

RESEARCH PRODUCT

Singular Double Phase Problems with Convection

Calogero VetroNikolaos S. PapageorgiouFrancesca Vetro

subject

ConvectionDirichlet problemPartial differential equationTruncationApplied Mathematics010102 general mathematicsMathematical analysisSingular termFixed pointMathematics::Spectral Theory01 natural sciencesTerm (time)Positive solution010101 applied mathematicsNonlinear system(p q)-LaplacianSettore MAT/05 - Analisi MatematicaNonlinear maximum principle0101 mathematicsLaplace operatorNonlinear regularityMathematics

description

We consider a nonlinear Dirichlet problem driven by the sum of a $p$ -Laplacian and of a $q$ -Laplacian (double phase equation). In the reaction we have the combined effects of a singular term and of a gradient dependent term (convection) which is locally defined. Using a mixture of variational and topological methods, together with suitable truncation and comparison techniques, we prove the existence of a positive smooth solution.

yearjournalcountryeditionlanguage
2020-09-30Acta Applicandae Mathematicae
https://doi.org/10.1007/s10440-020-00364-4