On $\mathcal{p}(x)$-Kirchhoff-type equation involving $\mathcal{p}(x)$-biharmonic operator via genus theory

S. Taarabti; Z.  El Allali; K.  Ben Haddouch

doi:10.37863/umzh.v72i6.6019

S. Taarabti Nat. School Appl. Sci. Agadir Ibn Zohr Univ., Morocco https://orcid.org/0000-0002-3134-9091
Z. El Allali Multidisciplinary Faculty of Nador, Mohammed First Univ., Oujda, Morocco
K. Ben Haddouch Nat. School Appl. Sci. Fes Sidi Mohammed Ben Abdellah Univ., Morocco

DOI: https://doi.org/10.37863/umzh.v72i6.6019

Анотація

УДК 517.9

Розглядаються проблеми iснування та множинностi нетривiальних слабких розв’язкiв $\mathcal{p}(x)$-задачi типу Кiрхгофа

$$ {-M}\!\left(\displaystyle\int\limits_{\Omega}\frac{1}{p(x)}|\Delta u|^{p(x)}\,dx\right)\!\Delta_{p(x)}^{2} u = f(x,u)\quad \mbox{in}\quad \Omega, $$

$$ u = \Delta u = 0\quad \mbox{on}\quad \partial\Omega.$$

Використовуючи варiацiйний пiдхiд та теорiю роду Красносельського, ми доводимо iснування та множиннiсть розв’язкiв для $\mathcal{p}(x)$-рiвняння типу Кiрхгофа.

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