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Variational Approach to Fourth-Order Impulsive Differential Equations with Two Control Parameters

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Abstract

In this paper, we are concerned with the multiplicity of solutions for a fourth-order impulsive differential equation with Dirichlet boundary conditions and two control parameters. Using variational methods and a three critical points theorem, we give some new criteria to guarantee that the impulsive problem has at least three classical solutions. We also provide an example in order to illustrate the main abstract results of this paper.

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Authors and Affiliations

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

    Ghasem A. Afrouzi & Armin Hadjian

  2. Institute of Mathematics “Simion Stoilow”, of the Romanian Academy, P.O. Box 1-764, 014700, Bucharest, Romania

    Vicenţiu D. Rădulescu

  3. Department of Mathematics, University of Craiova, Street A.I. Cuza No. 13, 200585, Craiova, Romania

    Vicenţiu D. Rădulescu

Authors
  1. Ghasem A. Afrouzi
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  2. Armin Hadjian
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  3. Vicenţiu D. Rădulescu
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Correspondence to Vicenţiu D. Rădulescu.

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Afrouzi, G.A., Hadjian, A. & Rădulescu, V.D. Variational Approach to Fourth-Order Impulsive Differential Equations with Two Control Parameters. Results. Math. 65, 371–384 (2014). https://doi.org/10.1007/s00025-013-0351-5

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  • DOI: https://doi.org/10.1007/s00025-013-0351-5

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