Infinitely many solutions and asymptotics for resonant oscillatory problems
Fuente:
arXiv
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| Autori principali: | , |
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| Natura: | Preprint |
| Pubblicazione: |
2025
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| _version_ | 1866918262009233408 |
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| author | Korman, Philip Schmidt, Dieter S. |
| author_facet | Korman, Philip Schmidt, Dieter S. |
| contents | For a class of oscillatory resonant problems, involving Dirichlet problems for semilinear PDE's on balls and rectangles in $R^n$, we show the existence of infinitely many solutions, and study the global solution set. The first harmonic of the right hand side is not required to be zero, or small. We also derive asymptotic formulas in terms of the first harmonic of solutions, and illustrate their accuracy by numerical computations. The numerical method is explained in detail. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_20816 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Infinitely many solutions and asymptotics for resonant oscillatory problems Korman, Philip Schmidt, Dieter S. Analysis of PDEs Functional Analysis 35J25, 35J61, 65N25 For a class of oscillatory resonant problems, involving Dirichlet problems for semilinear PDE's on balls and rectangles in $R^n$, we show the existence of infinitely many solutions, and study the global solution set. The first harmonic of the right hand side is not required to be zero, or small. We also derive asymptotic formulas in terms of the first harmonic of solutions, and illustrate their accuracy by numerical computations. The numerical method is explained in detail. |
| title | Infinitely many solutions and asymptotics for resonant oscillatory problems |
| topic | Analysis of PDEs Functional Analysis 35J25, 35J61, 65N25 |
| url | https://arxiv.org/abs/2512.20816 |