(untitled) (Analysis in Theory and Applications, 2025)
Abstract. In this paper we study the following nonlinear Schrödinger system: \[ cases -Δ u + a(x) u = λ(x) f(u, v), & x R^N, -Δ v + b(x) v = λ(x) g(u, v), & x R^N, u(x) → 0, & v(x) → 0 cases \] as |x| → ∞ . Here, a, b, λ C(R^N, R) are all non-periodic in x_i for i = 1, …, N, N ≥ 3, f, g C(R^2, R) . We show that this system has infinitely many solutions with small negative energies and infinitely many large-energy solutions. To the best of our knowledge, there is no corresponding result about such a Schrödinger system.