Geodesic
Infinitely many solutions for boundary value problems arising from the fractional advection dispersion equation
Applications of Mathematics, Tome 60 (2015) no. 6, pp. 703-724.

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We consider the existence of infinitely many solutions to the boundary value problem \begin {gather} \frac {{\rm d}}{{\rm d} t}\Big (\frac {1}{2} _{0}D_{t}^{-\beta }(u'(t)) +\frac {1}{2} _{t}D_{T}^{-\beta }(u'(t))\Big )+\nabla F(t,u(t))=0 \quad \text {\rm a.e.}\ t\in [0,T],\nonumber \\ u(0)=u(T)=0.\nonumber \end {gather} Under more general assumptions on the nonlinearity, we obtain new criteria to guarantee that this boundary value problem has infinitely many solutions in the superquadratic, subquadratic and asymptotically quadratic cases by using the critical point theory.
DOI : 10.1007/s10492-015-0118-2
Classification : 26A33, 35G60
Keywords: fractional boundary value problem; critical point theory; variational methods 
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Chen, Jing; Tang, Xian Hua. Infinitely many solutions for boundary value problems arising from the fractional advection dispersion equation. Applications of Mathematics, Tome 60 (2015) no. 6, pp. 703-724. doi : 10.1007/s10492-015-0118-2. http://geodesic.mathdoc.fr/articles/10.1007/s10492-015-0118-2/

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