Infinitely many positive solutions of fractional boundary value problems

Bin Ge, Vicenţiu D. Rădulescu, C. J. Zhang

DOI: http://dx.doi.org/10.12775/TMNA.2017.001

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).

Keywords


Fractional differential equation; oscillatory nonlinearities; infinitely many solutions; variational methods

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