Infinitely many solutions and asymptotics for resonant oscillatory problems

2025/12/23 by Korman, Philip, Schmidt, Dieter S.
#35J25 #35J61 #65N25 #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA)

paper · doi:10.48550/arxiv.2512.20816

Abstract

For a class of oscillatory resonant problems, involving Dirichlet problems for semilinear PDE's on balls and rectangles in Rⁿ, 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.

Citations

• Continuation of global solution curves using global parameters

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