## EXISTENCE AND MULTIPLICITY OF WEAK SOLUTIONS FOR PERTURBED KIRCHHOFF TYPE ELLIPTIC PROBLEMS WITH HARDY POTENTIAL

## *S. P. Roudbari, G. A. Afrouzi*

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## Abstract

In this paper, we prove the existence of at least three weak solutions for a doubly eigenvalue elliptic systems involving the p-biharmonic equation with Hardy potential of Kirchho type with Navier boundary condition. More precisely, by using variational methods and three critical points theorem due to B. Ricceri, we establish multiplicity results on the existence of weak solutions for such problems where the reaction term is a nonlinearity function f which satises in the some convenient growth conditions. Indeed, using a consequence of the critical point theorem due to Ricceri, which in it the coercivity of the energy Euler functional was required and is important, we attempt the existence of multiplicity solutions for our problem under algebraic conditions on the nonlinear parts. We also give an explicit example to illustrate the obtained result.

## Keywords

Multiplicity of weak solutions, perturbed Kirchho type elliptic problems, Hardy potential, Critical points.