| Summary: | 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.
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