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Nonlinear Nonhomogeneous Elliptic Problems

In: Current Trends in Mathematical Analysis and Its Interdisciplinary Applications

Author

Listed:
  • Nikolaos S. Papageorgiou

    (Department of Mathematics, National Technical University)

  • Calogero Vetro

    (Department of Mathematics and Computer Science, University of Palermo)

  • Francesca Vetro

    (Ton Duc Thang University, Nonlinear Analysis Research Group
    Ton Duc Thang University, Faculty of Mathematics and Statistics)

Abstract

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.

Suggested Citation

  • Nikolaos S. Papageorgiou & Calogero Vetro & Francesca Vetro, 2019. "Nonlinear Nonhomogeneous Elliptic Problems," Springer Books, in: Hemen Dutta & Ljubiša D. R. Kočinac & Hari M. Srivastava (ed.), Current Trends in Mathematical Analysis and Its Interdisciplinary Applications, chapter 0, pages 647-713, Springer.
    • Handle: RePEc:spr:sprchp:978-3-030-15242-0_17
    DOI: 10.1007/978-3-030-15242-0_17
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