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December 2016 Multiplicity result for a stationary fractional reaction-diffusion equations
César E. Torres Ledesma
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Tbilisi Math. J. 9(2): 115-127 (December 2016). DOI: 10.1515/tmj-2016-0024

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

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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

Received: 23 August 2016; Accepted: 7 October 2016; Published: December 2016
First available in Project Euclid: 12 June 2018

zbMATH: 1361.35202
MathSciNet: MR3578791
Digital Object Identifier: 10.1515/tmj-2016-0024

Subjects:
Primary: 26A33
Secondary: 30E25, 34A08

Rights: Copyright © 2016 Tbilisi Centre for Mathematical Sciences

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Vol.9 • No. 2 • December 2016
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