The interactions between hyperon-nucleon and hyperon-hyperon have been an important topic in strangeness nuclear physics, which play an important role in understanding the properties of hypernuclei and equation of state of strangeness nuclear matter. It is very difficult to perform a direct scattering experiment of the nucleon and hyperon because the short lifetime of the hyperon. Therefore, the hyperon-nucleon interaction and the hyperon-hyperon interaction have been mainly investigated experimentally by \gamma spectroscopy of single-\Lambda hypernuclei or double-\Lambda hypernuclei. There are also many theoretical methods developed to describe the properties of hypernuclei. Most of these models focus mostly on the ground state properties of hypernuclei, and have given exciting results in producing the banding energy, the energy of single-particle levels, deformations, and other properties of hypernuclei. Only a few researches adopting Skyrme energy density functionals is devoted to the study of the collective excitation properties of hypernuclei. In present work, we have extended the relativistic mean field and relativistic random phase approximation theories to study the collective excitation properties of hypernuclei, and use the methods to study the isoscalar collective excited state properties of double \Lambda hypernuclei. First, the effect of \Lambda hyperons on the single-particle energy of ¹⁶O and ^18_\Lambda\Lambda\rmO are discussed in the relativistic mean field theory, the calculations are performed within TM1 parameter set and related hyperon-nucleon interaction, and hyperon-hyperon interaction. We find that it gives a larger attractive effect on the \mathrms_1/2 state of proton and neutron, while gives a weaker attractive effect on the state around Fermi surface. The self-consistent relativistic random phase approximation is used to study the collectively excited state properties of hypernucleus ^18_\Lambda\Lambda\rmO. The isoscalar giant monopole resonance and quadrupole resonance are calculated and analysed in detail, we pay more attention to the effect of the inclusion of \Lambda hyperons on the properties of giant resonances. Comparing with the strength distributions of ¹⁶O, changes of response function of ^18_\Lambda\Lambda\rmO are evidently found both on the isoscalar giant monopole resonance and quadrupole resonance. It is shown that the difference comes mainly from the change of Hartree energy of particle-hole configuration and the contribution of the excitations of \Lambda hyperons. We find that the hyperon-hyperon residual interactions have small effect on the monopole resonance function and quadrupole response function in the low-energy region, and have almost no effect on the response functions in the high-energy region.