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

  • Ghasem A. Afrouzi EMAIL logo and Armin Hadjian
Published/Copyright: February 9, 2019

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.

Acknowledgements

The authors warmly thank the anonymous referees for their useful and nice comments on the manuscript.

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Received: 2017-12-14
Published Online: 2019-02-09
Published in Print: 2018-12-19

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