Infinitely many solutions and asymptotics for resonant oscillatory problems

Fuente: arXiv
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Autori principali: Korman, Philip, Schmidt, Dieter S.
Natura: Preprint
Pubblicazione: 2025
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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