具位势项的非齐次四阶Schrödinger方程的适定性研究

夏素霞, 李烁

doi:10.13371/j.cnki.chin.q.j.m.2026.01.007

数学季刊 >

2026 , Vol. 41 >Issue 1: 82 - 91

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2026.01.007

具位势项的非齐次四阶Schrödinger方程的适定性研究

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School of Mathematics and Statistics, Henan University of Technology, Zhengzhou 450001, China

XIA Su-xia (1982-), female, native of Puyang, Henan, associate professor of Henan University of Technology, engages in partial differential equation; LI Shuo (2001-), female, native of Zhoukou, Henan, postgraduate student of Henan University of Technology, engages in partial differential equation.

XIA Su-xia (1982-), female, native of Puyang, Henan, associate professor of Henan University of Technology, engages in partial differential equation;

收稿日期: 2025-08-11

网络出版日期: 2026-03-30

基金资助

Supported by National Natural Science Foundation of China (Grant No. 11601122).

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Global Well-Posedness for the Inhomogeneous Fourth-Order Schrödinger Equation with Potential

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School of Mathematics and Statistics, Henan University of Technology, Zhengzhou 450001, China

XIA Su-xia (1982-), female, native of Puyang, Henan, associate professor of Henan University of Technology, engages in partial differential equation;

Received date: 2025-08-11

Online published: 2026-03-30

Supported by

Supported by National Natural Science Foundation of China (Grant No. 11601122).

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摘要

The paper considers the initial value problem of inhomogeneous fourth-order Schrödinger equation with potential in energy space H²(R^d). The global well-posedness is obtained in dimensions d≥5 resorting to contractive mapping principle, Strichartz estimates, Caffarelli-Kohn-Nirenberg-type inequality and the continuity method.

关键词： Well-posedness; Inhomogeneous fourth-order Schr?dinger equation; Potential; Strichartz estimates; Continuity method

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夏素霞, 李烁 . 具位势项的非齐次四阶Schrödinger方程的适定性研究[J]. 数学季刊, 2026 , 41(1) : 82 -91 . DOI: 10.13371/j.cnki.chin.q.j.m.2026.01.007

Abstract

Key words： Well-posedness; Inhomogeneous fourth-order Schr?dinger equation; Potential; Strichartz estimates; Continuity method

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