Solutions to a Class of Disturbed Quasilinear Schrödinger Equations without Compactness
Journal Title: 河南科技大学学报（自然科学版） - Year 2019, Vol 40, Issue 4
Abstract
The existence of ground state solutions for a class of quasilinear Schrödinger equations with disturbance term was studied through Nehari manifold method. Firstly, it was proved that the Nehari manifold corresponding to the equation was non-empty by using an algebraic equation. Secondly, according to the definition of manifold and the Sobolev inequality, the norm of the elements had a positive lower bound when the Nehari manifold was limited. And then, the lack problem of compactness in the working space was solved by the concentration compactness principle. Thus, the functional constraint minimum corresponding to the equation was obtained. Finally, the existence of the ground state solution of the equation was obtained by using the constrained extremum principle.
Authors and Affiliations
Jinfeng GAO, Zhanping LIANG
Keywords
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- DOI 10.15926/j.cnki.issn1672-6871.2019.04.016
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