Discrete Schrödinger equations and systems with mixed and concave-convex nonlinearities

Chen, Guanwei; Ma, Shiwang

doi:10.1090/proc/16834

Discrete Schrödinger equations and systems with mixed and concave-convex nonlinearities
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by Guanwei Chen and Shiwang Ma;

Proc. Amer. Math. Soc. 152 (2024), 2621-2636

DOI: https://doi.org/10.1090/proc/16834

Published electronically: April 23, 2024

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Abstract:

In this paper, we obtain the existence of at least two standing waves (and homoclinic solutions) for a class of time-dependent (and time-independent) discrete nonlinear Schrödinger systems or equations. The novelties of the paper are as follows. (1) Our nonlinearities are composed of three mixed growth terms, i.e., the nonlinearities are composed of sub-linear, asymptotically-linear and super-linear terms. (2) Our nonlinearities may be sign-changing. (3) Our results can also be applied to the cases of concave-convex nonlinear terms. (4) Our results can be applied to a wide range of mathematical models.

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