Multiple Solutions for Nonlocal Fourth-Order Equation with Concave–Convex Nonlinearities

Ruiting Jiang and Chengbo Zhai ()
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Ruiting Jiang: College of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030031, China
Chengbo Zhai: School of Mathematics and Statistics, Shanxi University, Taiyuan 030006, China

Mathematics, 2025, vol. 13, issue 12, 1-12

Abstract: This paper is devoted to a class of general nonlocal fourth-order elliptic equation with concave–convex nonlinearities. First, using the Z 2 -mountain pass theorem in critical point theory, we obtain the existence of infinitely many large energy solutions. Then, using the dual fountain theorem, we prove that the equation has infinitely many negative energy solutions, whose energy converges at 0. Our results extend and complement existing findings in the literature.

Keywords: biharmonic operator; variational methods; Z2-mountain pass theorem; dual fountain theorem (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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