6533b82bfe1ef96bd128ce2d

RESEARCH PRODUCT

Nonlinear Nonhomogeneous Elliptic Problems

Nikolaos S. PapageorgiouFrancesca VetroCalogero Vetro

subject

Strong comparison principles(p 2)-equationsMultiplicity theoremsNodal solutionsDifferential operatorDirichlet distributionNonlinear systemsymbols.namesakeMaximum principleSettore MAT/05 - Analisi MatematicaNeumann boundary conditionsymbolsApplied mathematicsBoundary value problemNonlinear maximum principleLaplace operatorNonlinear regularityMorse theoryMathematics

description

We consider nonlinear elliptic equations driven by a nonhomogeneous differential operator plus an indefinite potential. The boundary condition is either Dirichlet or Robin (including as a special case the Neumann problem). First we present the corresponding regularity theory (up to the boundary). Then we develop the nonlinear maximum principle and present some important nonlinear strong comparison principles. Subsequently we see how these results together with variational methods, truncation and perturbation techniques, and Morse theory (critical groups) can be used to analyze different classes of elliptic equations. Special attention is given to (p, 2)-equations (these are equations driven by the sum of a p- Laplacian and a Laplacian), where stronger results can be stated.

yearjournalcountryeditionlanguage
2019-01-01
https://doi.org/10.1007/978-3-030-15242-0_17