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

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Abstract

We consider the existence of infinitely many solutions to the boundary value Problem

$\frac{d} {{dt}}\left( {\frac{1} {2}0D_t^{ - \beta } (u'(t)) + \frac{1} {2}tD_T^{ - \beta } (u'(t))} \right) + \nabla F(t,u(t)) = 0a.e.t \in [0,T],u(0) = u(T) = 0.$

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.

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Authors and Affiliations

  1. School of Mathematics and Computing Sciences, Hunan University of Science and Technology, Xiangtan, Hunan, 411201, P.R. China

    Jing Chen

  2. School of Mathematics and Statistics, Central South University, Changsha, Hunan, 410083, P.R. China

    Xian Hua Tang

Authors
  1. Jing Chen
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  2. Xian Hua Tang
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Corresponding author

Correspondence to Xian Hua Tang.

Additional information

The work was supported by the NSFC (No. 11501190) and Hunan Provincial Natural Science Foundation (No. 2015JJ6037) and by Scientific Research Fund of Hunan Provincial Education Department (No. 14C0465).

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Chen, J., Tang, X.H. Infinitely many solutions for boundary value problems arising from the fractional advection dispersion equation. Appl Math 60, 703–724 (2015). https://doi.org/10.1007/s10492-015-0118-2

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  • DOI: https://doi.org/10.1007/s10492-015-0118-2

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