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On the p(X)-Kirchhoff-Type Equation Involving the p(X)-Biharmonic Operator via the Genus Theory

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Ukrainian Mathematical Journal Aims and scope

The paper deals with the existence and multiplicity of nontrivial weak solutions for the p(x)-Kirchhofftype problem

$$ {\displaystyle \begin{array}{c}-M\left(\underset{\Omega}{\int}\frac{1}{p(x)}{\left|\Delta u\right|}^{p(x)} dx\right){\Delta}_{p(x)}^2u=f\left(x,u\right)\kern0.6em \mathrm{in}\kern0.48em \Omega, \\ {}u=\Delta u=0\kern0.48em \mathrm{on}\kern0.48em \mathrm{\partial \Omega }.\end{array}} $$

By using the variational approach and the Krasnosel’skii genus theory, we prove the existence and multiplicity of solutions for the p(x)-Kirchhoff-type equation.

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Author information

Authors and Affiliations

  1. National School of Applied Sciences, University Ibnou Zohr, Agadir, Morocco

    S. Taarabti

  2. Multidisciplinary Faculty of Nador, Mohammed I University, Oujda, Morocco

    Z. El Allali

  3. National School of Applied Sciences, Sidi Mohammed Ben Abdellah University, Fes, Morocco

    K. Ben Haddouch

Authors
  1. S. Taarabti
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  2. Z. El Allali
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  3. K. Ben Haddouch
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Corresponding author

Correspondence to S. Taarabti.

Additional information

Published in Ukrains’kyi Matematychnyi Zhurnal, Vol. 72, No. 6, pp. 842–851, June, 2020. Ukrainian DOI: 10.37863/umzh.v72i6.6019.

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Taarabti, S., El Allali, Z. & Haddouch, K.B. On the p(X)-Kirchhoff-Type Equation Involving the p(X)-Biharmonic Operator via the Genus Theory. Ukr Math J 72, 978–989 (2020). https://doi.org/10.1007/s11253-020-01836-4

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  • DOI: https://doi.org/10.1007/s11253-020-01836-4

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