Zobrazeno 1 - 10
of 57
pro vyhledávání: '"Rainer Mandel"'
Publikováno v:
Comptes Rendus. Mathématique, 360 (G5), 513–538
In this paper, we study nonlinear Helmholtz equations with sign-changing diffusion coefficients on bounded domains. The existence of an orthonormal basis of eigenfunctions is established making use of weak -coercivity theory. All eigenvalues are prov
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::f7f2f35de7925c249ffdfa694494df0e
https://doi.org/10.5802/crmath.322
https://doi.org/10.5802/crmath.322
Autor:
Rainer Mandel, Dominic Scheider
Publikováno v:
Nonlinearity. 34:3618-3640
We construct infinitely many real-valued, time-periodic breather solutions of the nonlinear wave equation ∂ t t U − Δ U = Q ( x ) | U | p − 2 U on T × R N with suitable N ⩾ 2, p > 2 and localized nonnegative Q. These solutions are obtained
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::36095f64a3c069f12e47ebe597c9f4cc
https://doi.org/10.1088/1361-6544/abed38
https://doi.org/10.1088/1361-6544/abed38
Publikováno v:
Journal of Dynamics and Differential Equations. 34:2201-2227
In this paper we investigate the effect of nonlinear damping on the Lugiato–Lefever equation $$\mathrm {i}\partial _t a = -(\mathrm {i}-\zeta ) a - da_{xx} -(1+\mathrm {i}\kappa )|a|^2a +\mathrm {i}f$$ on the torus or the real line. For the case of
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::f3da32870d4a8cc4139249ae10af8d7f
https://doi.org/10.1007/s10884-021-09943-x
https://doi.org/10.1007/s10884-021-09943-x
Autor:
Rainer Mandel, Robert Schippa
Publikováno v:
Annales Henri Poincaré, 23, 1831–1882
We solve time-harmonic Maxwell's equations in anisotropic, spatially homogeneous media in intersections of $L^p$-spaces. The material laws are time-independent. The analysis requires Fourier restriction-extension estimates for perturbations of Fresne
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::5907b78a9c4473242953c48491647cc9
https://publikationen.bibliothek.kit.edu/1000141756/139694532
https://publikationen.bibliothek.kit.edu/1000141756/139694532
Autor:
Rainer Mandel
Publikováno v:
Advanced Nonlinear Studies. 19:569-593
We obtain uncountably many solutions of nonlinear Helmholtz and curl-curl equations on the entire space using a fixed point approach. The constructed solutions are mildly localized as they lie in the essential spectrum of the corresponding linear ope
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_________::91b9d770695c83031051aefcf7586ee0
https://doi.org/10.1515/ans-2019-2050
https://doi.org/10.1515/ans-2019-2050
Autor:
Rainer Mandel
Publikováno v:
Communications in Mathematical Physics. 368:799-842
We prove an $L^p$-version of the limiting absoprtion principle for a class of periodic elliptic differential operators of second order. The result is applied to the construction of nontrivial solutions of nonlinear Helmholtz equations with periodic c
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::bca8e85b16f7a7514c9cb71ac92207ac
https://doi.org/10.1007/s00220-019-03363-1
https://doi.org/10.1007/s00220-019-03363-1
Publikováno v:
Calculus of variations and partial differential equations, 60 (4), Article no: 133
We prove new existence results for a nonlinear Helmholtz equation with sign-changing nonlinearity of the form $$\begin{aligned} - \Delta u - k^{2}u = Q(x)|u|^{p-2}u, \quad u \in W^{2,p}\left( {\mathbb {R}}^{N}\right) \end{aligned}$$ - Δ u - k 2 u =
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::34e880a030e15e68125515bdec593844
Autor:
Rainer Mandel, Dominic Scheider
We consider the Helmholtz equation $$-\Delta u+V \, u - \lambda \, u = f $$ on $${\mathbb {R}}^n$$ where the potential $$V:{\mathbb {R}}^n\rightarrow {\mathbb {R}}$$ is constant on each of the half-spaces $${\mathbb {R}}^{n-1}\times (-\infty ,0)$$ an
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::4164928ae16947e51ca18981fb0864c5
http://arxiv.org/abs/2001.07465
http://arxiv.org/abs/2001.07465
Publikováno v:
Journal of Differential Equations
Journal of Differential Equations, 2022, 330, pp.1-65. ⟨10.1016/j.jde.2022.04.037⟩
Journal of Differential Equations, 2022, 330, pp.1-65. ⟨10.1016/j.jde.2022.04.037⟩
We study the standing waves for a fourth-order Schr\"odinger equation with mixed dispersion that minimize the associated energy when the $L^2-$norm (the \textit{mass}) } is kept fixed. We need some non-homogeneous Gagliardo-Nirenberg-type inequalitie
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::84e25179782b52f0ef3d0f50937b95a5
Autor:
Rainer Mandel
Publikováno v:
Pure Appl. Anal. 2, no. 2 (2020), 519-532
The initial value problem for the homogeneous Schr\"odinger equation is investigated for radially symmetric initial data with slow decay rates and not too wild oscillations. Our global wellposedness results apply to initial data for which Strichartz
Externí odkaz:
https://explore.openaire.eu/search/publication?articleId=doi_dedup___::250028f162b3eb689233c599935d1009
http://arxiv.org/abs/1910.05973
http://arxiv.org/abs/1910.05973