No CrossRef data available.
Article contents
Necessary and sufficient conditions for ground state solutions to planar Kirchhoff-type equations
Published online by Cambridge University Press: 11 March 2024
Abstract
In this paper, we are concerned with the ground states of the following planar Kirchhoff-type problem: are constants, $p>2$
. Based on variational methods, regularity theory and Schwarz symmetrization, the equivalence of ground state solutions for the above problem with the minimizers for some minimization problems is obtained. In particular, a new scale technique, together with Lagrange multipliers, is delicately employed to overcome some intrinsic difficulties.
- Type
- Research Article
- Information
- Copyright
- Copyright © The Author(s), 2024. Published by Cambridge University Press on behalf of The Royal Society of Edinburgh
References
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240308141104504-0258:S030821052400026X:S030821052400026X_inline347.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240308141104504-0258:S030821052400026X:S030821052400026X_inline348.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240308141104504-0258:S030821052400026X:S030821052400026X_inline349.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240308141104504-0258:S030821052400026X:S030821052400026X_inline350.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240308141104504-0258:S030821052400026X:S030821052400026X_inline351.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240308141104504-0258:S030821052400026X:S030821052400026X_inline352.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240308141104504-0258:S030821052400026X:S030821052400026X_inline353.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240308141104504-0258:S030821052400026X:S030821052400026X_inline354.png?pub-status=live)
![](https://static.cambridge.org/binary/version/id/urn:cambridge.org:id:binary:20240308141104504-0258:S030821052400026X:S030821052400026X_inline355.png?pub-status=live)