Nonlinear Nonhomogeneous Elliptic Problems

Nikolaos S. Papageorgiou (), Calogero Vetro () and Francesca Vetro ()
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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

Chapter Chapter 17 in Current Trends in Mathematical Analysis and Its Interdisciplinary Applications, 2019, pp 647-713 from Springer

Abstract: 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.

Keywords: Nonlinear regularity; Nonlinear maximum principle; Strong comparison principles; Multiplicity theorems; Nodal solutions; (p; 2)-equations (search for similar items in EconPapers)
Date: 2019
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Persistent link: https://EconPapers.repec.org/RePEc:spr:sprchp:978-3-030-15242-0_17

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DOI: 10.1007/978-3-030-15242-0_17

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