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The existence of least energy nodal solutions for some class of Kirchhoff equations and Choquard equations in RN

Hongyu Ye - No affiliation found

2015/11/15 Full-length article DOI: 10.1016/j.jmaa.2015.06.012 Journal: Journal of Mathematical Analysis and Applications

Abstract:

AbstractIn this paper, we study the existence of least energy nodal solutions for a class of Kirchhoff type problems in RN. Since the 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 in RN and show that the sign-changing solution has an energy strictly larger than the least energy and less than twice the least energy.