Existence of weak solutions for nonlocal Schr\"{o}dinger--Kirchhoff equations with the external magnetic field
Bull. Korean Math. Soc.
Published online November 2, 2021
Jae-Myoung Kim, Yun-Ho Kim, and Kisoeb Park
Andong National University; Sangmyung University; Seoul Theological University
Abstract : We study to show the existence of a nontrivial weak solution to Kirchhoff type equations involving the fractional magnetic field without Ambrosetti and Rabinowitz condition using mountain pass theorem under a suitable assumption of the external force. Also, we present the existence of infinitely many large- or small- energy solutions to this problem. The strategy of the proof for these results is to approach the problem variationally by applying the variational methods, namely, the fountain and the dual fountain theorem with Cerami condition.
Keywords : Schr\"{o}dinger-Kirchhoff equation, Fractional magnetic operators, Variational methods.
MSC numbers : 58E05, 26A33, 35J60, 47G20
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