In this paper, we study the following (p,q)-Laplacian equation: \(\left\{ \begin{aligned}&-\Delta _{p}u - \Delta _{q}u = \lambda |u|^{p-2}u + |u|^{\overline{q}-2}u + \mu |u|^{t-2}u,&\int _{\mathbb {R}^{N}} |u|^{p}dx = a^{p}, \end{aligned} \right. \) where \(1< p< q < N\) , \(\Delta _{i} = \text {div}(|\nabla u|^{i-2} \nabla u)\) for \(i \in \{ p, q \}\) is the \(i\) -Laplacian operator, \(\lambda \) is a Lagrange multiplier, \(\overline{q} = q + \frac{pq}{N}\) is the \(L^p\) -critical exponent, \(\mu \in \mathbb {R}^{+}\) and \(p< t < p^{*} = \frac{Np}{N-p}\) . In the \(L^p\) -critical case, the different values of t affect the geometric structure of the functional corresponding to the equation. The purpose of this paper is to establish the existence of radial normalized solution on different t.
