Dual variational methods for a nonlinear Helmholtz equation with sign-changing nonlinearity
- We prove new existence results for a nonlinear Helmholtz equation with sign-changing nonlinearity of the form − delta u−k2u=Q(x)/u/p−2u, uEW2, p(RN) – delta u − k2u=Q(x)/u/p−2u, uEW2, p(RN) with k>0, k>0, N≥3N≥3, pE[2(N+1)N − 1, 2NN − 2)pE[2(N+1)N − 1, 2NN−2) and QEL ∞ (RN)QEL ∞ (RN). Due to the sign-changes of Q, our solutions have infinite Morse-Index in the corresponding dual variational formulation.
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| Author: | Rainer Mandel, Dominic Scheider, Tolga Yeşil |
|---|---|
| URN: | urn:nbn:de:hebis:30:3-637719 |
| DOI: | https://doi.org/10.1007/s00526-021-02006-5 |
| ISSN: | 1432-0835 |
| Parent Title (English): | Calculus of variations and partial differential equations |
| Publisher: | Springer |
| Place of publication: | Berlin ; Heidelberg |
| Document Type: | Article |
| Language: | English |
| Date of Publication (online): | 2021/06/29 |
| Date of first Publication: | 2021/06/29 |
| Publishing Institution: | Universitätsbibliothek Johann Christian Senckenberg |
| Release Date: | 2022/06/15 |
| Volume: | 60 |
| Issue: | art. 133 |
| Page Number: | 13 |
| First Page: | 1 |
| Last Page: | 13 |
| Note: | The first two authors are funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)-Project-ID 258734477—SFB 1173. |
| Note: | Open Access funding enabled and organized by Projekt DEAL. |
| HeBIS-PPN: | 497501546 |
| Institutes: | Informatik und Mathematik |
| Dewey Decimal Classification: | 5 Naturwissenschaften und Mathematik / 51 Mathematik / 510 Mathematik |
| MSC-Classification: | 35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Jxx Elliptic equations and systems [See also 58J10, 58J20] / 35J20 Variational methods for second-order elliptic equations |
| 35-XX PARTIAL DIFFERENTIAL EQUATIONS / 35Qxx Equations of mathematical physics and other areas of application [See also 35J05, 35J10, 35K05, 35L05] / 35Q60 PDEs in connection with optics and electromagnetic theory | |
| Sammlungen: | Universitätspublikationen |
| Licence (German): |  Creative Commons - Namensnennung 4.0 |
