Abstract
In this paper, we consider the stationary fractional reaction-diffusion equations with Riemann-Liouville boundary conditions $$\begin{aligned} &{_{x}}D_{T}^{\alpha}({_{0}}D_{x}^{\alpha}u(x)) + {_{0}}D_{x}^{\beta}({_{x}}D_{T}^{\beta}u(x)) = f(x,u(x)),\;\;x\in (0,T),\\ &\lim_{x\to 0} {_{0}}I_{x}^{1-\alpha}u(x) = \lim_{x\to T} {_{x}}I_{T}^{1-\beta}u(x) = 0. \end{aligned}$$
(0.1)
where $0\lt \alpha , \beta \lt 1$ and $f\in C([0,T] \times \mathbb{R}, \mathbb{R})$. Under suitable conditions on the nonlinearity $f$, we study the multiplicity of weak solutions of (0.1) by using the genus in the critical point theory.
Citation
César E. Torres Ledesma. "Multiplicity result for a stationary fractional reaction-diffusion equations." Tbilisi Math. J. 9 (2) 115 - 127, December 2016. https://doi.org/10.1515/tmj-2016-0024
Information