The existence of least energy nodal solutions for some class of Kirchhoff equations and Choquard equations
By Hongyu Ye. 2015
59 citations recorded by the source corpus.
In this paper, we study the existence of least energy nodal solutions for some class of Kirchhoff type problems. Since Kirchhoff equation is a nonlocal one, the variational setting to look for sign-changing solutions is different from the local cases. By using constrained minimization on the sign-changing Nehari manifold, we prove the Kirchhoff problem has a least energy nodal solution with its energy exceeding twice the least energy. As a co-product of our approaches, we obtain the existence of least energy sign-changing solution for Choquard equations and show that the sign-changing solution has an energy strictly larger than the least energy and less than twice the least energy.
Subfields: Applied Mathematics, Computational Theory and Mathematics, Control and Systems Engineering
View Paper: https://www.semanticscholar.org/paper/45670035c6fae37514374000fe48664f60315981
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In Applied Mathematics
- Jean Van Schaftingen
- Marco Ghimenti
- Vitaly Moroz
- Hongyu Ye
- Minbo Yang
- Franz Gmeineder
- Bogdan Raiță
- Jiankang Xia
In Computational Theory and Mathematics
In Control and Systems Engineering
Citations in the corpus
- Nodal solutions for the Choquard equation (2015, background): “Nodal solutions which minimize the action among radial solutions were constructed [26].”