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1. Discrete Schr\"{o}dinger equations and systems with mixed and concave-convex nonlinearities.

Author

Chen, Guanwei and Ma, Shiwang

Subjects
*NONLINEAR equations, *STANDING waves, *NONLINEAR Schrodinger equation, *MOUNTAIN pass theorem, *SCHRODINGER equation, *MATHEMATICAL models
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. [ABSTRACT FROM AUTHOR]

Published
2024
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