#### Angela M. Koester, Jeffrey T. Neugebauer, Smallest eigenvalues for fractional boundary value problems with a fractional boundary condition, Vol. 2017 (2017), Article ID 1, pp. 1-16

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DOI: 10.23952/jnfa.2017.1

Received July 20, 2016; Accepted  October 10, 2016

Abstract. Let $n\in\mathbb{N}$, $n\ge 2$. For $n-1<\alpha\le n$, we use the theory of $u_0$-positive operators to show the existence of and then compare smallest eigenvalues of the fractional boundary value problems $D^\alpha_{0^+} u + \lambda_1 p(t) u=0$, $D^\alpha_{0^+} u + \lambda_2 q(t) u=0$, $0, satisfying boundary conditions $u^{(i)}(0)=0$, $i=0,1,\dots,n-2$, $D^\beta_{0^+} u(1)=0$, $0\le\beta\le n-1$, where p and q are nonnegative continuous functions on $[0,1]$ which do not vanish identically on any nondegenerate compact subinterval of $[0,1]$. The cases where $\beta=0$ and $\beta>0$ are treated separately and then compared.

How to Cite this Article:

Angela M. Koester, Jeffrey T. Neugebauer, Smallest eigenvalues for fractional boundary value problems with a fractional boundary condition, Journal Nonlinear Functional Analysis, Vol. 2017 (2017), Article ID 1, pp. 1-16.