TY - JOUR
T1 - Multiple Solutions for a Fractional $p$-Laplacian Equation with Concave Nonlinearities
AU - Pei , Ruichang
JO - Journal of Partial Differential Equations
VL - 2
SP - 93
EP - 108
PY - 2020
DA - 2020/05
SN - 33
DO - http://doi.org/10.4208/jpde.v33.n2.1
UR - https://global-sci.org/intro/article_detail/jpde/16853.html
KW - Fractional $p$-Laplacian problems, Morse theory, concave nonlinearities, existence and multiplicity of solutions.
AB - <p style="text-align: justify;">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&lt;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.</p>