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Volume 10
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10.3390/math10152736
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Article

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

by
Jintao He
and
Tingjian Luo
*
School of Mathematics and Information Sciences, Guangzhou University, Guangzhou 510006, China
*
Author to whom correspondence should be addressed.
Mathematics 2022, 10(15), 2736; https://doi.org/10.3390/math10152736
Submission received: 7 July 2022 / Revised: 27 July 2022 / Accepted: 28 July 2022 / Published: 2 August 2022
(This article belongs to the Special Issue Nonlinear Differential Equations and Functional Analysis: Theory and Applications)
Versions Notes

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 fourth-order equation; ground states; asymptotic behaviors; energy estimates

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MDPI and ACS Style

He, J.; Luo, T. Existence and Asymptotic Behaviors of Ground States for a Fourth-Order Nonlinear Schrödinger Equations with a Potential. Mathematics 2022, 10, 2736. https://doi.org/10.3390/math10152736

AMA Style

He J, Luo T. Existence and Asymptotic Behaviors of Ground States for a Fourth-Order Nonlinear Schrödinger Equations with a Potential. Mathematics. 2022; 10(15):2736. https://doi.org/10.3390/math10152736

Chicago/Turabian Style

He, Jintao, and Tingjian Luo. 2022. "Existence and Asymptotic Behaviors of Ground States for a Fourth-Order Nonlinear Schrödinger Equations with a Potential" Mathematics 10, no. 15: 2736. https://doi.org/10.3390/math10152736

APA Style

He, J., & Luo, T. (2022). Existence and Asymptotic Behaviors of Ground States for a Fourth-Order Nonlinear Schrödinger Equations with a Potential. Mathematics, 10(15), 2736. https://doi.org/10.3390/math10152736

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