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Zbl 1193.34008
Zhao, Xiangkui; Ge, Weigao
Unbounded solutions for a fractional boundary value problems on the infinite interval. (English)
[J] Acta Appl. Math. 109, No. 2, 495-505 (2010). ISSN 0167-8019; ISSN 1572-9036/e

Summary: We consider the fractional boundary value problem $$\cases D^{a}_{0+}u(t)+f(t,u(t))=0,\quad t\in(0,\infty), \alpha\in (1,2),\\ u(0)=0,\quad\lim_{t\rightarrow\infty}D^{a-1}_{0+}u(t)=\beta u(\xi), \endcases$$ where $D$ is the standard Riemann-Liouville fractional derivative. By means of fixed point theorems, sufficient conditions are obtained that guarantee the existence of solutions to the above boundary value problem.

MSC 2000:: *34A08
34B18 Positive solutions of nonlinear boundary value problems
34B40 Boundary value problems on infinite intervals
47N20 Appl. of operator theory to differential and integral equations

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