Positive solutions for nonlinear Schrödinger–Kirchhoff equations in R3. (June 2020)

• Record Type: Journal Article
• Authors: Chen, Wei; Fu, Zunwei; Wu, Yue
• Is Part Of: Applied mathematics letters. Volume 104(2020)
• Publication Date: 2020-06
• Subjects: Schrödinger–Kirchhoff-type equations -- Variational methods -- Lagrange multiplier rule -- Pohozaev equality; Applied mathematics -- Periodicals; 519.05
• DOI: 10.1016/j.aml.2020.106274
• Languages: English
• ISSNs: 0893-9659

Abstract

Abstract: In this paper, we study the nonlinear Schrödinger–Kirchhoff-type equation with pure power nonlinearities in R 3 by variational methods. By carrying out the constrained minimization on a special manifold which is a combination of the Nehari manifold and Pohozaev manifold, we proved the existence of positive radial solutions of this equation for the power p ∈ ( 1, 5 ) . The results of this paper extend some existing conclusions, especially for p ∈ ( 1, 2 ] .