## Topological Methods in Nonlinear Analysis

### Infinitely many positive solutions of fractional boundary value problems

#### Abstract

We are concerned with the qualitative analysis of solutions of a class of fractional boundary value problems with Dirichlet boundary conditions. By combining a direct variational approach with the theory of the fractional derivative spaces, we establish the existence of infinitely many distinct positive solutions whose $E^\alpha$-norms and $L^\infty$-norms tend to zero (to infinity, respectively) whenever the nonlinearity oscillates at zero (at infinity, respectively).

#### Article information

Source
Topol. Methods Nonlinear Anal., Volume 49, Number 2 (2017), 647-664.

Dates
First available in Project Euclid: 10 March 2017

https://projecteuclid.org/euclid.tmna/1489114815

Digital Object Identifier
doi:10.12775/TMNA.2017.001

Mathematical Reviews number (MathSciNet)
MR3670480

Zentralblatt MATH identifier
1375.35181

#### Citation

Ge, Bin; Rădulescu, Vicențiu D.; Zhang, Ji-Chun. Infinitely many positive solutions of fractional boundary value problems. Topol. Methods Nonlinear Anal. 49 (2017), no. 2, 647--664. doi:10.12775/TMNA.2017.001. https://projecteuclid.org/euclid.tmna/1489114815