caa a22 4500 605515182 CHVBK 20210128100707.0 cr unu---uuuuu 210128e20150101xx s 000 0 eng 10.1007/s00205-014-0778-1 doi (NATIONALLICENCE)springer-10.1007/s00205-014-0778-1 Ground and Bound State Solutions of Semilinear Time-Harmonic Maxwell Equations in a Bounded Domain [Elektronische Daten] [Thomas Bartsch, Jarosław Mederski] We find solutions $${E : \Omega \to \mathbb{R}^3}$$ E : Ω → R 3 of the problem $$\left\{\begin{aligned}&\nabla \times(\nabla \times E) + \lambda E = \partial_E F(x, E) &&\quad \text{in }\quad \Omega \\& \nu \times E = 0 &&\quad \text{on }\quad \partial \Omega \end{aligned} \right.$$ ∇ × ( ∇ × E ) + λ E = ∂ E F ( x , E ) in Ω ν × E = 0 on ∂ Ω on a simply connected, smooth, bounded domain $${\Omega \subset \mathbb{R}^3}$$ Ω ⊂ R 3 with connected boundary and exterior normal $${\nu : \partial \Omega \to \mathbb{R}^3}$$ ν : ∂ Ω → R 3 . Here $${\nabla \times}$$ ∇ × denotes the curl operator in $${\mathbb{R}^3}$$ R 3 , the nonlinearity $${F : \Omega \times \mathbb{R}^3 \to \mathbb{R}}$$ F : Ω × R 3 → R is superquadratic and subcritical in E. The model nonlinearity is of the form $${F(x, E)=\Gamma(x) |E|^p}$$ F ( x , E ) = Γ ( x ) | E | p for $${\Gamma \in L^\infty(\Omega)}$$ Γ ∈ L ∞ ( Ω ) positive, some 2<p<6. It need not be radial nor even in the E-variable. The problem comes from the time-harmonic Maxwell equations, the boundary conditions are those for Ω surrounded by a perfect conductor. Springer-Verlag Berlin Heidelberg, 2014 Bartsch Thomas Mathematisches Institut, Universität Giessen, Arndtstr. 2, 35392, Giessen, Germany aut Mederski Jarosław Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100, Toruń, Poland aut Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 215/1(2015-01-01), 283-306 0003-9527 215:1<283 2015 215 205 https://doi.org/10.1007/s00205-014-0778-1 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s00205-014-0778-1 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Bartsch Thomas Mathematisches Institut, Universität Giessen, Arndtstr. 2, 35392, Giessen, Germany aut NATIONALLICENCE 700 1- Mederski Jarosław Faculty of Mathematics and Computer Science, Nicolaus Copernicus University, ul. Chopina 12/18, 87-100, Toruń, Poland aut NATIONALLICENCE 773 0- Archive for Rational Mechanics and Analysis Springer Berlin Heidelberg 215/1(2015-01-01), 283-306 0003-9527 215:1<283 2015 215 205