Year: 2020
Author: Ruichang Pei
Journal of Partial Differential Equations, Vol. 33 (2020), Iss. 2 : pp. 93–108
Abstract
We investigate a fractional $p$-Laplacian equation with right-hand-side nonlinearity which exhibits $(p-1)$-sublinear term of the form $\lambda |u|^{q-2},\, q<p $ (concave term), and a continuous term $f(x,u)$ which is respectively $(p-1)$-superlinear or asymptotically $(p-1)$-linear at infinity. Some existence results for multiple nontrivial solutions are established by using variational methods combined with the Morse theory.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/jpde.v33.n2.1
Journal of Partial Differential Equations, Vol. 33 (2020), Iss. 2 : pp. 93–108
Published online: 2020-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 16
Keywords: Fractional $p$-Laplacian problems Morse theory concave nonlinearities existence and multiplicity of solutions.