Quasilinear Dirichlet problems with competing operators and convection
Dumitru Motreanu
Abstract
Abstract The paper deals with a quasilinear Dirichlet problem involving a competing ( p , q )-Laplacian and a convection term. Due to the lack of ellipticity, monotonicity and variational structure, the known methods to find a weak solution are not applicable. We develop an approximation procedure permitting to establish the existence of solutions in a generalized sense. If in place of competing ( p , q )-Laplacian we consider the usual ( p , q )-Laplacian, our results ensure the existence of weak solutions.
Topics & Concepts
Monotonic functionMathematicsDirichlet distributionLaplace operatorApplied mathematicsConvectionDirichlet problemTerm (time)Pure mathematicsMathematical analysisPhysicsQuantum mechanicsMeteorologyBoundary value problemNonlinear Partial Differential EquationsAdvanced Mathematical Modeling in EngineeringSpectral Theory in Mathematical Physics