In this work, we study the existence and multiplicity of solutions to the problem $$\displaylines{ -(\Delta)_p^s u + V(x)|u|^{p-2}u = \lambda f(u),\quad x\in\Omega;\cr u=0,\quad x\in \mathbb{R}^N\backslash\Omega, }$$ where \(\Omega\subset\mathbb{R}^N\) is an open bounded set with Lipschitz boundary \(\partial\Omega\), \(N\geqslant 2\), \(V\in L^{\infty}(\mathbb{R}^N)\), and \((-\Delta)_p^s\) denotes the fractional p-Laplacian with \(s\in(0,1)\), \(1<p\), \(sp<N\), \(\lambda>0\), and \(f:\mathbb{R}\to\mathbb{R}\) is a continuous function. We extend the results of Lopera et al [22] by proving the existence of a second weak solution to this problem. We apply a variant of the mountain-pass theorem due to Hofer [15] and infinite-dimensional Morse theory to obtain the existence of at least two solutions. For more information see https://ejde.math.txstate.edu/Volumes/2024/72/abstr.html