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<p>In this paper, we consider the Schrödinger type equation −Δ<i>u</i> + <i>V</i> (<i>x</i>)<i>u</i> = <i>f</i>(<i>x, u</i>) on the lattice graph ℤ<sup><i>N</i></sup> with indefinite variational functional, where Δ is the discrete Laplacian. Specifically, we assume that <i>V</i> (<i>x</i>) and <i>f</i>(<i>x, u</i>) are periodic in <i>x, f</i> satisfies some growth condition and 0 lies in a finite spectral gap of (−Δ + <i>V</i>). We obtain ground state solutions by using the method of generalized Nehari manifold which has been introduced by Pankov.</p>

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Ground State Solutions to Some Indefinite Nonlinear Schrödinger Equations on Lattice Graphs

  • 期刊论文

  • 发表日期：

    2025年5月15日

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  • Wendi Xu

摘要

In this paper, we consider the Schrödinger type equation −Δu + V (x)u = f(x, u) on the lattice graph ℤN with indefinite variational functional, where Δ is the discrete Laplacian. Specifically, we assume that V (x) and f(x, u) are periodic in x, f satisfies some growth condition and 0 lies in a finite spectral gap of (−Δ + V). We obtain ground state solutions by using the method of generalized Nehari manifold which has been introduced by Pankov.