Tbilisi Mathematical Journal

Multiplicity result for a stationary fractional reaction-diffusion equations

César E. Torres Ledesma

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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.

Article information

Source
Tbilisi Math. J., Volume 9, Issue 2 (2016), 115-127.

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

Permanent link to this document
https://projecteuclid.org/euclid.tbilisi/1528769072

Digital Object Identifier
doi:10.1515/tmj-2016-0024

Mathematical Reviews number (MathSciNet)
MR3578791

Zentralblatt MATH identifier
1361.35202

Subjects
Primary: 26A33: Fractional derivatives and integrals
Secondary: 34A08: Fractional differential equations 30E25: Boundary value problems [See also 45Exx]

Keywords
Riemann-Liouville fractional derivatives fractional derivative space boundary value problem genus variational methods

Citation

Ledesma, César E. Torres. Multiplicity result for a stationary fractional reaction-diffusion equations. Tbilisi Math. J. 9 (2016), no. 2, 115--127. doi:10.1515/tmj-2016-0024. https://projecteuclid.org/euclid.tbilisi/1528769072


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