Dual ground state solutions for the critical nonlinear Helmholtz equation
Yazarlar (2)
Gilles Evéquoz Goethe-Universität Frankfurt Am Main, Almanya
Doç. Dr. Tolga Acar YEŞİL Goethe-Universität Frankfurt Am Main, Almanya
| Makale Türü | Özgün Makale (SSCI, AHCI, SCI, SCI-Exp dergilerinde yayınlanan tam makale) | ||
| Dergi Adı | Proceedings of the Royal Society of Edinburgh Section A Mathematics (Q2) | ||
| Dergi ISSN | 0308-2105 Dergi Bilgileri (2020) | ||
| Makale Dili | İngilizce | Basım Tarihi | 06-2020 |
| Kabul Tarihi | – | Yayınlanma Tarihi | 30-01-2019 |
| Cilt / Sayı / Sayfa | 150 / 3 / 1155–1186 | DOI | 10.1017/prm.2018.103 |
| Makale Linki | https://arxiv.org/pdf/1707.00959.pdf | ||
| UAK Araştırma Alanları |
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| Özet |
| Using a dual variational approach, we obtain nontrivial real-valued solutions of the critical nonlinear Helmholtz equation for -Δu - k2u = Q(x)|u|2 ∗-2u, u ϵ W2,2∗ (ℝN) N ≥ 4, where 2∗ : = 2N/(N - 2). The coefficient is assumed to be nonnegative, asymptotically periodic and to satisfy a flatness condition at one of its maximum points. The solutions obtained are so-called dual ground states, that is, solutions arising from critical points of the dual functional with the property of having minimal energy among all nontrivial critical points. Moreover, we show that no dual ground state exists for N = 3. |
| Anahtar Kelimeler |
| critical exponent | dual variational method | nonexistence results | Nonlinear Helmholtz equation | nonvanishing |
Science Direct
Dual ground state solutions for the critical nonlinear Helmholtz equation
BM Sürdürülebilir Kalkınma Amaçları
| Atıf Sayıları | |
| Scopus | 11 |