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sublinear

Proceedings of the Royal Society of Edinburgh Section A: Mathematics (1)

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Perturbed Schrödinger lattice systems: existence of homoclinic solutions
Part of
Guanwei Chen, Shiwang Ma
Journal:

Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 149 / Issue 4 / August 2019

Published online by Cambridge University Press:

27 December 2018, pp. 1083-1096

Print publication:

August 2019
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We study a class of Schrödinger lattice systems with sublinear nonlinearities and perturbed terms. We get an interesting result that the systems do not have nontrivial homoclinic solutions if the perturbed terms are removed, but the systems have ground state homoclinic solutions if the perturbed terms are added. Besides, we also study the continuity of the homoclinic solutions in the perturbation terms at zero. To the best of our knowledge, there is no published result focusing on the perturbed Schrödinger lattice systems.