Observation of e$^{+}$e$^{-}$ -> π$^{+}$π$^{-}$π$^{0}$χ$_{b1,2}$(1$\textit{P}$) and search for e$^{+}$e$^{-}$ -> ϕχ$_{b1,2}$(1$\textit{P}$) at $\sqrt{s}$ = 10.96$-$11.05 GeV

We report searches for the processes e$^{+}$e$^{-}$ → π$^{+}$π$^{-}$π$^{0}$χ$_{bj}$ and e$^{+}$e$^{-}$ → ϕχ$_{bj}$ (J=1, 2) based on data samples collected by the Belle experiment at the KEKB collider. We report the first observation of the process e$^{+}$e$^{-}$ → $^{+}$π$^{-}$π$^{0}$$_{non−ωχb1}$ and first evidence for e$^{+}$e$^{-}$ → ωχbJ in the vicinity of the Υ(11020) resonance, with center-of-mass energies from 10.96 to 11.05 GeV. The significances for $^{+}$π$^{-}$π$^{0}$$_{non−ωχb1}$ and ωχbJ are greater than 5.3σ and 4.0σ, respectively. We also investigate the energy dependence of the e$^{+}$e$^{-}$ →$^{+}$π$^{-}$π$^{0}$χbJ cross section, but we cannot determine whether the contributions are from the Υ(10860) and Υ(11020) resonances or nonresonant continuum processes. The signals for e$^{+}$e$^{-}$ → ϕ$_{χbj}$ are not significant, and the upper limits of the Born cross sections at the 90% confidence level are 0.7 and 1.0 pb for e$^{+}$e$^{-} → ϕχb1 and ϕχb2, respectively, for center-of-mass energies from 10.96 to 11.05 GeV.