A Class of Fourth-Order Symmetrical Kirchhoff Type Systems

This paper deals with the existence and multiplicity of solutions for a perturbed nonlocal fourth-order class of p(·)&q(·)-Kirchhoff elliptic systems under Navier boundary conditions. By using the variational method and Ricceri’s critical point theorem, we can find a proper conditions to ensure...

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Bibliographic Details
Published inSymmetry (Basel) Vol. 14; no. 8; p. 1630
Main Authors Wu, Yong, Taarabti, Said, El Allali, Zakaria, Ben Hadddouch, Khalil, Zuo, Jiabin
Format Journal Article
LanguageEnglish
Published Basel MDPI AG 01.08.2022
Subjects
(p(x), q(x))-Kirchhoff system
Banach spaces
Boundary conditions
Critical point
multiple solutions
Norms
p(x)-biharmonic operator
Partial differential equations
three critical points theory
variational method
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Summary:This paper deals with the existence and multiplicity of solutions for a perturbed nonlocal fourth-order class of p(·)&q(·)-Kirchhoff elliptic systems under Navier boundary conditions. By using the variational method and Ricceri’s critical point theorem, we can find a proper conditions to ensure that the perturbed fourth-order of (p(x),q(x))-Kirchhoff systems has at least three weak solutions. We have extended and improved some recent results. The complexity of the combination of variable exponent theory and fourth-order Kirchhoff systems makes the results of this work novel and new contribution. Finally, a very concrete example is given to illustrate the applications of our results.
ISSN:2073-8994
2073-8994
DOI:10.3390/sym14081630