Multiplicity of solutions for fractional p-Laplacian equation with indefinite nonlinearity

ABSTRACT

We study the existence and multiplicity of positive solutions for the quasi-linear problem $\{\begin{array}{ll}(-{\mathrm{\Delta }}_p{)}^{s}u=\lambda {|u|}^{p-2}u+a(x){|u|}^{q-2}u& \mathrm{i}\mathrm{n}\mathrm{\Omega },\\ u=0& \mathrm{i}\mathrm{n}{\mathbb{R}}^N\setminus \mathrm{\Omega },\end{array}$ where Ω is a bounded domain in ${\mathbb{R}}^N$, λ a real parameter, 1<p<q and a changes sign.

KEYWORDS:

• Fractional p-Laplacian
• indefinite nonlinearity
• positive solutions
• multiple solutions

AMS SUBJECT CLASSIFICATIONS:

• 35R11
• 35A15

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

F. O. de Paiva was supported by São Paulo Research Foundation (FAPESP), Brazil. D. Rodriguez Villena was supported by CAPES (Brazil).