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<p>In this paper, we obtain the existence of negative and positive energy homoclinic solutions for perturbed discrete nonlinear Schrödinger systems with combined nonlinearities by using variational methods. The main novelties of the paper are as follows. (1) Our results cover the cases of perturbed terms and combined nonlinearities (i.e., concave–convex terms, two sub-linear terms, or sub-linear and asymptotically linear terms). (2) Our weight functions may be sign-changing. (3) Our potentials are periodic or non-periodic but bounded. (4) Our energy functional may be indefinite. (5) The result of the continuity of solutions is obtained in the case of perturbation terms at zero.</p>

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Multiple solutions of discrete Schrödinger systems with perturbed and combined nonlinearities

  • 期刊论文

  • 发表日期：

    2025年4月25日

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  • Guanwei Chen,
  • Lixun Jia

摘要

In this paper, we obtain the existence of negative and positive energy homoclinic solutions for perturbed discrete nonlinear Schrödinger systems with combined nonlinearities by using variational methods. The main novelties of the paper are as follows. (1) Our results cover the cases of perturbed terms and combined nonlinearities (i.e., concave–convex terms, two sub-linear terms, or sub-linear and asymptotically linear terms). (2) Our weight functions may be sign-changing. (3) Our potentials are periodic or non-periodic but bounded. (4) Our energy functional may be indefinite. (5) The result of the continuity of solutions is obtained in the case of perturbation terms at zero.