Existence and Asymptotic Behaviors of Ground States for a Fourth-Order Nonlinear Schrödinger Equations with a Potential

Jintao He and Tingjian Luo
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Jintao He: School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China
Tingjian Luo: School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China

Mathematics, 2022, vol. 10, issue 15, 1-10

Abstract: In this paper, we study the existence and asymptotic behaviors of ground state solutions to a fourth-order nonlinear Schrödinger equation with mass-critical exponent, where the fourth-order term appears as a perturbation with ε > 0 . By considering a constrained variational problem, we first establish the existence of ground state solutions. Then, we prove the asymptotic behaviors of the solutions as ε → 0 + . The main ingredients of the proofs are some energy estimate arguments. Our results improve somewhat the ones in the existing reference.

Keywords: fourth-order equation; ground states; asymptotic behaviors; energy estimates (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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