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AN IMPROVED RESULT ON GROUND STATE SOLUTIONS OF QUASILINEAR SCHRÖDINGER EQUATIONS WITH SUPER-LINEAR NONLINEARITIES

Part of: Elliptic equations and systems Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  26 December 2018

SITONG CHEN Open the ORCID record for SITONG CHEN [Opens in a new window]  and
ZU GAO
SITONG CHEN*
Affiliation:
School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, PR China email [email protected]
ZU GAO
Affiliation:
School of Mathematics and Statistics, Central South University, Changsha, Hunan 410083, PR China email [email protected]
*
✉[email protected]
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Abstract

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By using variational and some new analytic techniques, we prove the existence of ground state solutions for the quasilinear Schrödinger equation with variable potentials and super-linear nonlinearities. Moreover, we establish a minimax characterisation of the ground state energy. Our result improves and extends the existing results in the literature.

Keywords

quasilinear Schrödinger equationground state solutionPohoz̆aev identity

MSC classification

Primary: 35J20: Variational methods for second-order elliptic equations
Secondary: 35Q55: NLS-like equations (nonlinear Schrödinger)
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 99 , Issue 2 , April 2019 , pp. 231 - 241
Copyright
© 2018 Australian Mathematical Publishing Association Inc. 

Footnotes

This work is partially supported by the National Natural Science Foundation of China (11571370, 11701487 and 11626202) and Hunan Provincial Natural Science Foundation of China (2016JJ6137).

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