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Volume 33, Issue 2
Multiple Solutions for a Fractional $p$-Laplacian Equation with Concave Nonlinearities

Ruichang Pei

DOI: 10.4208/jpde.v33.n2.1

J. Part. Diff. Eq., 33 (2020), pp. 93-108.

Published online: 2020-05

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  • 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.

  • Keywords

Fractional $p$-Laplacian problems, Morse theory, concave nonlinearities, existence and multiplicity of solutions.

  • AMS Subject Headings

34A08, 35Q40, 58E05

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address

prc211@163.com (Ruichang Pei)

  • BibTex
  • RIS
  • TXT
@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} }
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 -

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.

Ruichang Pei. (2020). Multiple Solutions for a Fractional $p$-Laplacian Equation with Concave Nonlinearities. Journal of Partial Differential Equations. 33 (2). 93-108. doi:10.4208/jpde.v33.n2.1
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