Zhouji Ma, Xiaojun Chang, Zhaosheng Feng
Abstract:
We study the existence of normalized ground state solutions to a mixed dispersion
fourth-order nonlinear Schrodinger equation with combined power-type nonlinearities.
By analyzing the subadditivity of the ground state energy with respect to the
prescribed mass, we employ a constrained minimization method to establish the
existence of ground state that corresponds to a local minimum of the associated
functional. Under certain conditions, by studying the monotonicity of ground state
energy as the mass varies, we apply the constrained minimization arguments on the
Nehari-Pohozaev manifold to prove the existence of normalized ground state solutions.
Submitted November 18, 2023. Published April 1, 2024
Math Subject Classifications: 35Q55, 31B30, 35J30.
Key Words: Normalized solutions; Schrodinger equation; Lagrange multiplier; ground states; Nehari-Pohozaev manifold.
DOI: 10.58997/ejde.2024.29
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Zhouji Ma School of Mathematics and Statistics Northeast Normal University Changchun, Jilin 130024, China email: mazj588@nenu.edu.cn |
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Xiaojun Chang School of Mathematics and Statistics and Center for Mathematics and Interdisciplinary Sciences Northeast Normal University Changchun, Jilin 130024, China email: changxj100@nenu.edu.cn |
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Zhaosheng Feng School of Mathematical and Statistical Sciences University of Texas Rio Grande Valley Edinburg, TX 78539, USA email: zhaosheng.feng@utrgv.edu |
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