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Ground state solutions for asymptotically linear Schrödinger equations on locally finite graphs
  • Yunxue Li,
  • Zhengping Wang
Yunxue Li
Wuhan University of Technology
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Zhengping Wang
Wuhan University of Technology

Corresponding Author:[email protected]

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We are considered with the following nonlinear Schrödinger equation −∆ u+( λa( x)+1) u= f( u) ,xV, on a locally finite graph G=( V,E), where V denotes the vertex set, E denotes the edge set, λ>1 is a parameter, f( s) is asymptotically linear with respect to s at infinity, and the potential a: V→[0 ,+∞) has a nonempty well Ω. By using variational methods we prove that the above problem has a ground state solution u λ for any λ>1. Moreover, we show that as λ→∞, the ground state solution u λ converges to a ground state solution of a Dirichlet problem defined on the potential well Ω.
Submitted to Mathematical Methods in the Applied Sciences
20 Mar 2024Editorial Decision: Revise Minor
30 Mar 2024Review(s) Completed, Editorial Evaluation Pending
03 Apr 2024Editorial Decision: Accept