Infinitely many solutions for boundary value problems arising from the fractional advection dispersion equation

[摘要] 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.

[学科分类] 应用数学

[关键词] fractional boundary value problem;critical point theory;variational methods