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A variational approach for boundary value problems for impulsive fractional differential equations

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Abstract

By using an abstract critical point result for differentiable and parametric functionals due to B. Ricceri, we establish the existence of infinitely many classical solutions for fractional differential equations subject to boundary value conditions and impulses. More precisely, we determine some intervals of parameters such that the treated problems admit either an unbounded sequence of solutions, provided that the nonlinearity has a suitable oscillatory behaviour at infinity, or a pairwise distinct sequence of solutions that strongly converges to zero if a similar behaviour occurs at zero. No symmetric condition on the nonlinear term is assumed. Two examples are then given.

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Authors and Affiliations

  1. Department of Mathematics, Faculty of Mathematical Sciences University of Mazandaran, Babolsar, Iran

    Ghasem A. Afrouzi

  2. Department of Mathematics, Faculty of Basic Sciences University of Bojnord, Bojnord, 94531, Iran

    Armin Hadjian

Authors
  1. Ghasem A. Afrouzi
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  2. Armin Hadjian
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Correspondence to Ghasem A. Afrouzi.

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Afrouzi, G.A., Hadjian, A. A variational approach for boundary value problems for impulsive fractional differential equations. FCAA 21, 1565–1584 (2018). https://doi.org/10.1515/fca-2018-0082

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