Korman, Philip2023-06-152023-06-152016-03-10Korman, P. (2016). Nonlinear elliptic equations and systems with linear part at resonance. Electronic Journal of Differential Equations, 2016(67), pp. 1-17.1072-6691https://hdl.handle.net/10877/16939The 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.Text17 pages1 file (.pdf)enAttribution 4.0 InternationalElliptic systems at resonanceResonance at multiple eigenvaluesLazer and Leach conditionArticle