Acta mathematica scientia,Series A ›› 2024, Vol. 44 ›› Issue (3): 637-649.

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Infinitely Many Large Energy Solutions for the Klein-Gordon-Born-Infeld Equation on $\mathbf{R}^3$ with Concave and Convex Nonlinearities

Chen Shangjie1,2()   

  1. 1. School of Mathematics and Statistics, Chongqing Technology and Business University, Chongqing 400067
    2. Chongqing Key Laboratory of Social Economy and Applied Statistics, Chongqing 400067
  • Received:2023-04-24 Revised:2023-09-27 Online:2024-06-26 Published:2024-05-17
  • Supported by:
    Team Building Project for Graduate Tutors in Chongqing(yds223010);CTBU Statistics Measure and Applications Group(ZDPTTD201909)

Abstract:

In this paper, we obtained the existence of infinitely many large energy solutions for the Klein-Gordon equation with concave and convex nonlinearities coupled with Born-Infeld theory on $\mathbb{R}^3$ by using $\mathbf{Z}_2$-Mountain Pass Theorem in critical point theory.

Key words: Klein-Gordon equation, Born-Infeld theory, Variational methods, $\mathbf{Z}_2$-Mountain Pass Theorem

CLC Number: 

  • O176.3
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