Authors
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Tao Zhang
Department of Lanzhou Technology and Business College, Lanzhou, Gansu 730101, People’s Republic of China
Author
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WeiQiang Zhang
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People’s Republic of China
Author
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Peihao Zhao
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People’s Republic of China
Author
Keywords:
Fractional p-Laplacian, Superlinear Reaction, Dirichlet Boundary, Variational Methods, Morse Theory
Abstract
This paper is dedicated to studying the following fractional p-Laplacian problem where Ω⊂ℝN (N ≥ 2) is a bounded domain with C 1,1 boundary, s∈(0,1), 2 ≤ p<N/s, (-Δ) sp is the fractional p-Laplacian and f is a (p-1) superlinearCarathéodory reaction but does not satisfy the usual Ambrosetti-Rabinowitz condition. By using variational methods and Morse theory, we show that the equation has at least three nontrivial solutions: among one of them is positive and one is negative.
Author Biographies
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Tao Zhang, Department of Lanzhou Technology and Business College, Lanzhou, Gansu 730101, People’s Republic of China
Department of Lanzhou Technology and Business College, Lanzhou, Gansu 730101, People’s Republic of China
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WeiQiang Zhang, School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People’s Republic of China
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People’s Republic of China
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Peihao Zhao, School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People’s Republic of China
School of Mathematics and Statistics, Lanzhou University, Lanzhou, Gansu 730000, People’s Republic of China
