A continuous-time input signal x(t) is an eigenfunction of an LTI system, if the output is

1
k x(t), where k is an eigenvalue
2
Keiωt x(t), where k is an eigenvalue and eiωt is a complex exponential signal
3
x(t) eiωt, where eiωt is a complex exponential signal
4
k H(ω), where k is an eigenvalue and H(ω) is a frequency response of the system
5
Ke-iωt x(t), where k is an eigenvalue and e-iωt is a complex exponential signal

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