In this paper, we investigate a class of quasilinear Schrödinger equations involving the Laplacian, a potential function V(x), and a nonlinear term that depends on a function f(x, u). The variable x belongs to \(\mathbb {R}^N\) , where \(N \ge 3\) . We impose suitable conditions on the parameter \(\tau \) (with \(\tau \ge 2\) ), the potential V (assumed to be continuous on \(\mathbb {R}^N\) ), and the nonlinearity f (assumed to be locally defined with respect to u near the origin). Under these assumptions, we establish the existence of infinitely many solutions in a neighborhood of the origin. An example is provided to illustrate the applicability of the main theoretical results.
