@Article{JPDE-33-93, author = {Pei , Ruichang}, title = {Multiple Solutions for a Fractional $p$-Laplacian Equation with Concave Nonlinearities}, journal = {Journal of Partial Differential Equations}, year = {2020}, volume = {33}, number = {2}, pages = {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.

}, issn = {2079-732X}, doi = {https://doi.org/10.4208/jpde.v33.n2.1}, url = {http://global-sci.org/intro/article_detail/jpde/16853.html} }