Tbilisi Mathematical Journal

Perturbed fourth-order Kirchho-type problems

Shapour Heidarkhani, Shahin Moradi, Giuseppe Caristi, and Bin Ge

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We establish the existence of at least three distinct weak solutions for a perturbed nonlocal fourth-order Kirchhoff-type problem with Navier boundary conditions under appropriate hypotheses on nonlinear terms. Our main tools are based on variational methods and some critical points theorems. We give some examples to illustrate the obtained results.

Article information

Tbilisi Math. J., Volume 11, Issue 4 (2018), 113-143.

Received: 8 March 2018
Accepted: 21 September 2018
First available in Project Euclid: 4 January 2019

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Mathematical Reviews number (MathSciNet)

Primary: 35J20: Variational methods for second-order elliptic equations
Secondary: 35J40: Boundary value problems for higher-order elliptic equations 35J35: Variational methods for higher-order elliptic equations 31B30: Biharmonic and polyharmonic equations and functions 35G30: Boundary value problems for nonlinear higher-order equations 74H20: Existence of solutions 35Q35: PDEs in connection with fluid mechanics

three distinct solutions fourth-order boundary value problem Kirchhoff-type problem Navier condition variational methods


Heidarkhani, Shapour; Moradi, Shahin; Caristi, Giuseppe; Ge, Bin. Perturbed fourth-order Kirchho-type problems. Tbilisi Math. J. 11 (2018), no. 4, 113--143. doi:10.32513/tbilisi/1546570890. https://projecteuclid.org/euclid.tbilisi/1546570890

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