Nonlinear elliptic equations and systems with linear part at resonance
Date
2016-03-10
Authors
Korman, Philip
Journal Title
Journal ISSN
Volume Title
Publisher
Texas State University, Department of Mathematics
Abstract
The famous result of Landesman and Lazer [10] dealt with resonance at a simple eigenvalue. Soon after publication of [10], Williams [14] gave an extension for repeated eigenvalues. The conditions in Williams [14] are rather restrictive, and no examples were ever given. We show that seemingly different classical result by Lazer and Leach [11], on forced harmonic oscillators at resonance, provides an example for this theorem. The article by Williams [14] also contained a shorter proof. We use a similar approach to study resonance for 2X2 systems. We derive conditions for existence of solutions, which turned out to depend on the spectral properties of the linear part.
Description
Keywords
Elliptic systems at resonance, Resonance at multiple eigenvalues, Lazer and Leach condition
Citation
Korman, P. (2016). Nonlinear elliptic equations and systems with linear part at resonance. Electronic Journal of Differential Equations, 2016(67), pp. 1-17.
Rights
Attribution 4.0 International