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- W3201788557 abstract "<abstract><p>In this article, we consider the following nonlocal fractional Kirchhoff-type elliptic systems</p> <p><disp-formula> <label/> <tex-math id=FE1> begin{document}$ begin{equation*} left{begin{array}{l} -M_{1}left(int_{mathbb{R}^{N}timesmathbb{R}^{N}}frac{|eta(x)-eta(y)|^{^{p(x, y)}}}{p(x, y)|x-y|^{N+p(x, y)s(x, y)}} dxdy +int_{Omega}frac{|eta|^{overline{p}(x)}}{overline{p}(x)}dxright) left(Delta_{p(cdot)}^{s(cdot)}eta-|eta|^{overline{p}(x)}etaright) ; ; ; = lambda F_{eta}(x, eta, xi)+mu G_{eta}(x, eta, xi), ; ; x in Omega, -M_{2}left(int_{mathbb{R}^{N}timesmathbb{R}^{N}}frac{|xi(x)-xi(y)|^{^{p(x, y)}}}{p(x, y)|x-y|^{N+p(x, y)s(x, y)}} dxdy +int_{Omega}frac{|xi|^{overline{p}(x)}}{overline{p}(x)}dxright) left(Delta_{p(cdot)}^{s(cdot)}xi-|xi|^{overline{p}(x)}xiright) ; ; ; = lambda F_{xi}(x, eta, xi)+mu G_{xi}(x, eta, xi), ; ; x in Omega, ; eta = xi = 0, ; ; x in mathbb{R}^{N}backslash Omega, end{array} right. end{equation*} $end{document} </tex-math></disp-formula></p> <p>where $ M_{1}(t), M_{2}(t) $ are the models of Kirchhoff coefficient, $ Omega $ is a bounded smooth domain in $ mathbb R^{N} $, $ (-Delta)_{p(cdot)}^{s(cdot)} $ is a fractional Laplace operator, $ lambda, mu $ are two real parameters, $ F, G $ are continuous differentiable functions, whose partial derivatives are $ F_{eta}, F_{xi}, G_{eta}, G_{xi} $. With the help of direct variational methods, we study the existence of solutions for nonlocal fractional $ p(cdot) $-Kirchhoff systems with variable-order, and obtain at least two and three weak solutions based on Bonanno's and Ricceri's critical points theorem. The outstanding feature is the case that the Palais-Smale condition is not requested. The major difficulties and innovations are nonlocal Kirchhoff functions with the presence of the Laplace operator involving two variable parameters.</p></abstract>" @default.
- W3201788557 created "2021-10-11" @default.
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- W3201788557 date "2021-01-01" @default.
- W3201788557 modified "2023-09-24" @default.
- W3201788557 title "Nonlocal fractional $ p(cdot) $-Kirchhoff systems with variable-order: Two and three solutions" @default.
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- W3201788557 doi "https://doi.org/10.3934/math.2021801" @default.
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