Opuscula Math. 37, no. 5 (2017), 755-772
http://dx.doi.org/10.7494/OpMath.2017.37.5.755

Opuscula Mathematica

# Multiplicity results for perturbed fourth-order Kirchhoff-type problems

Shapour Heidarkhani

Abstract. In this paper, we investigate the existence of three generalized solutions for fourth-order Kirchhoff-type problems with a perturbed nonlinear term depending on two real parameters. Our approach is based on variational methods.

Keywords: multiplicity results, multiple solutions, fourth-order Kirchhoff-type equation, variational methods, critical point theory.

Mathematics Subject Classification: 34B15, 58E05.

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• Islamic Azad University, Science and Research Branch, Department of Mathematics, Tehran, Iran
• Islamic Azad University, Qaemshahr Branch, Department of Mathematics, Qaemshahr, Iran
• Shapour Heidarkhani
• Razi University, Faculty of Sciences, Department of Mathematics, 67149 Kermanshah, Iran
• Communicated by Vicentiu D. Radulescu.
• Revised: 2016-12-27.
• Accepted: 2016-12-28.
• Published online: 2017-07-05.