Existence of multiple normalized solutions to a critical growth Choquard equation involving mixed operator

In this paper we study the normalized solutions of the following critical growth Choquard equation with mixed local and non-local operators: {equation*} {array}{rcl} -Δu +(-Δ)^s u & = & λu +μ|u|ᵖ⁻²u +(I_α*|u|2^*_α)|u|2^*_α-2u in R^N;\;\; \| u \|_2 & = & τ, {array} {equation*} here N≥ 3, $τ>0$, I_α is the Riesz potential of order α∈ (0,N), 2^*_α=N+α/N-2 is the critical exponent corresponding to the Hardy Littlewood Sobolev inequality, (-Δ)ˢ is the non-local fractional Laplacian operator with s∈ (0,1), $μ>0$ is a parameter and $λ$ appears as Lagrange multiplier. We have shown the existence of atleast two distinct solutions in the presence of mass subcritical perturbation, μ|u|ᵖ⁻²u with 2<p<2+4s/N under some assumptions on $τ$.