Annales Academiæ Scientiarum Fennicæ
Mathematica
Volumen 43, 2018, 293-310

THE ∞-FUCÍK SPECTRUM

Julio D. Rossi, Ariel M. Salort and João V. da Silva

FCEyN - Universidad de Buenos Aires, Departamento de Matemática and
IMAS - CONICET, Ciudad Universitaria, Pabellón I (1428) Av. Cantilo s/n.
Buenos Aires, Argentina; jrossi 'at' dm.uba.ar

FCEyN - Universidad de Buenos Aires, Departamento de Matemática and
IMAS - CONICET, Ciudad Universitaria, Pabellón I (1428) Av. Cantilo s/n.
Buenos Aires, Argentina; asalort 'at' dm.uba.ar

FCEyN - Universidad de Buenos Aires, Departamento de Matemática and
IMAS - CONICET, Ciudad Universitaria, Pabellón I (1428) Av. Cantilo s/n.
Buenos Aires, Argentina; jdasilva 'at' dm.uba.ar

Abstract. In this article we study the behavior as p ↑ ∞ of the Fucík spectrum for p-Laplace operator with zero Dirichlet boundary conditions in a bounded domain Ω ⊂ Rⁿ. We characterize the limit equation, and we provide a description of the limit spectrum. Furthermore, we show some explicit computations of the spectrum for certain configurations of the domain.

2010 Mathematics Subject Classification: Primary 35B27, 35J60, 35J70.

Key words: Fucík spectrum, degenerate fully nonlinear elliptic equations, infinity-Laplacian operator.

Reference to this article: J. D. Rossi, A. M. Salort and J. V. da Silva: The ∞-Fucík spectrum. Ann. Acad. Sci. Fenn. Math. 43 (2018), 293-310.

Full document as PDF file

https://doi.org/10.5186/aasfm.2018.4317