Special Issue in honor of Alan C. Lazer. Electron. J. Diff. Eqns., Special Issue 01 (2021), pp. 301-314.

Infinitely many solutions and asymptotics for resonant oscillatory problems

Philip Korman, Dieter S. Schmidt

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.

Published February 23, 2022.
Math Subject Classifications: 35J25, 35J61, 65N25.
Key Words: Global solution curves; asymptotic distribution of solutions.
DOI: https://doi.org/10.58997/ejde.sp.01.k1

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Philip Korman
Department of Mathematical Sciences
University of Cincinnati
Cincinnati, OH 45221-0025, USA
email: kormanp@ucmail.uc.edu
Dieter S. Schmidt
Department of Computer Science
University of Cincinnati
Cincinnati, OH 45221-0030, USA
email: schmiddr@ucmail.uc.edu

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