[{"type":"report","title":"Dual variational methods for an indefinte nonlinear Helmholtz equation","issued":{"date-parts":[["2020","11"]]},"DOI":"10.5445\/IR\/1000126434\/v2","author":[{"family":"Mandel","given":"Rainer"},{"family":"Scheider","given":"Dominic"},{"family":"Ye\u015fil","given":"Tolga"}],"publisher":"Karlsruher Institut f\u00fcr Technologie (KIT)","ISSN":"2365-662X","collection-title":"CRC 1173 Preprint","abstract":"We prove new existence results for a Nonlinear Helmholtz equation with sign-changing nonlinearity of the form $$-\\Delta u-k^2u=Q(x)|u|^{p-2}u,\\quad u\\in W^{2,p}(\\mathbb{R}^N)$$ with $k>0, N\\ge3,p\\in\\left[\\frac{2(N+1)}{N-1},\\frac{2N}{N-2}\\right]$ and $Q\\in L^\\infty(\\mathbb{R}^N)$. Due to sign-changes of $Q$, our solutions have infinite Morse-Index in the \r\ncorresponding dual variational formulation.","keyword":"indefinite variational problem, dual variational method, nonlinear Helmholtz equation, saddle-point reduction","number-of-pages":17,"kit-publication-id":"1000126434"}]