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Born-Infeld problem with general nonlinearity

Mederski, Jarosław; Pomponio, Alessio


In this paper, using variational methods, we look for non-trivial solutions for the following problem
$$\begin{cases}-\text{div}\left(a(|\nabla u|^2)\nabla u\right)=g(u), & \text{ in }\mathbb{R}^N, N \ge 3, \\ u(x) \to 0, & \text{ as } |x| \to +\infty\end{cases}$$
under general assumptions on the continuous nonlinearity $g$. We assume only growth conditions of $g$ at $0$, however no growth conditions at infinity are imposed. If $a(s) = (1−s)^{−1/2}$ , we obtain the well-known Born-Infeld operator, but we are able to study also a general class of a such that $a(s) \to +\infty$ as $s \to 1^{-}$. We find a radial solution to the problem with finite energy.

Volltext §
DOI: 10.5445/IR/1000137942
Veröffentlicht am 27.09.2021
Cover der Publikation
Zugehörige Institution(en) am KIT Institut für Analysis (IANA)
Sonderforschungsbereich 1173 (SFB 1173)
Publikationstyp Forschungsbericht/Preprint
Publikationsmonat/-jahr 09.2021
Sprache Englisch
Identifikator ISSN: 2365-662X
KITopen-ID: 1000137942
Verlag Karlsruher Institut für Technologie (KIT)
Umfang 17 S.
Serie CRC 1173 Preprint ; 2021/38
Projektinformation SFB 1173/2 (DFG, DFG KOORD, SFB 1173/2 2019)
Externe Relationen Siehe auch
Schlagwörter Born-Infeld theory, mean curvature operator, Lorentz-Minkowski space, nonlinear scalar field equation, variational methods
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