Multiple normalized solutions for fractional (p,q)-Laplacian equations in R^N

In this article, we consider the multiplicity results of normalized solutions of the fractional $(p,q)$-Laplacian equation $$\displaylines{ (-\Delta)_p^{s} u+(-\Delta)_q^{s} u=\lambda |u|^{p-2}u+h(\varepsilon x)f(u)+g(u) \quad\text{in }\mathbb{R}^N,\cr \int_{\mathbb {R}^{N}}|u|^p \mathrm{d}x=a^p, }$$ where \(\varepsilon, a >0\), \(0< s< 1< p< q\), \(sq< N< \frac{spq(q-1)}{q-p}\) and \(\lambda \in \mathbb {R}\) is a unknown Lagrange multiplier, \(h\) is a continuous positive function, \(f\) and \(g\) are also continuous and satisfy some growth conditions. When \(\varepsilon\) is small enough, we show that the number of normalized solutions is at least the number of global maximum points of \(h\) according to the Ekeland's variational principle and the concentration compactness principle. For more information and the latex file, see https://ejde.math.txstate.edu/Volumes/2026/14/abstr.html