Existence results for perturbed fourth-order Kirchhoff type elliptic problems with singular term

Ahmad Ghazvehi; Ghasem A. Afrouzi

doi:10.5269/bspm.44841

Ahmad Ghazvehi University of Mazandaran
Ghasem A. Afrouzi University of Mazandaran http://orcid.org/0000-0001-8794-3594

Abstract

Under appropriate growth conditions on the nonlinearity, the existence of multiple solutions for a perturbed
nonlocal fourth-order Kirchhoff-type problem involving the Hardy term:$$\Delta_p ^2 u-\big[M(\int_{\Omega}|\nabla u|^{p}dx)\big]^{p-1}\Delta_{p}u-\mu\frac{|u|^{p-2}u}{|x|^{2p}}= \lambda f(x,u),$$is established. Our main tools are based on variational methods and some critical points
theorems. We give some examples to illustrate the obtained results.

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