Opuscula Math. 36, no. 5 (2016), 631-649
http://dx.doi.org/10.7494/OpMath.2016.36.5.631

Opuscula Mathematica

# Multiplicity results for an impulsive boundary value problem of p(t)-Kirchhoff type via critical point theory

A. Mokhtari
T. Moussaoui
D. O'Regan

Abstract. In this paper we obtain existence results of $$k$$ distinct pairs nontrivial solutions for an impulsive boundary value problem of $$p(t)$$-Kirchhoff type under certain conditions on the parameter $$\lambda$$.

Keywords: genus theory, nonlocal problems, impulsive conditions, Kirchhoff equation, $$p(t)$$-Laplacian, variational methods, critical point theory.

Mathematics Subject Classification: 35A15, 35B38, 34A37.

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• A. Mokhtari
• Laboratory of Fixed Point Theory and Applications, Department of Mathematics, E.N.S. Kouba, Algiers, Algeria
• T. Moussaoui
• Laboratory of Fixed Point Theory and Applications, Department of Mathematics, E.N.S. Kouba, Algiers, Algeria
• D. O'Regan
• School of Mathematics, Statistics and Applied Mathematics, National University of Ireland, Galway, Ireland
• Communicated by Marek Galewski.
• Revised: 2016-03-12.
• Accepted: 2016-03-30.
• Published online: 2016-06-29.