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- W3157840812 abstract "In this paper, we consider the strongly coupled nonlinear Kirchhoff-type system with vanshing potentials: begin{equation*}begin{cases} -left(a_1+b_1int_{mathbb{R}^3}|nabla u|^2dxright)Delta u+lambda V(x)u=frac{alpha}{alpha+beta}|u|^{alpha-2}u|v|^{beta},&xinmathbb{R}^3, -left(a_2+b_2int_{mathbb{R}^3}|nabla v|^2dxright)Delta v+lambda W(x)v=frac{beta}{alpha+beta}|u|^{alpha}|v|^{beta-2}v,&xinmathbb{R}^3, u,vin mathcal{D}^{1,2}(R^3), end{cases}end{equation*} where $a_i>0$ are constants, $lambda,b_i>0$ are parameters for $i=1,2$, $alpha,beta>1$ and $alpha+betaleqslant 4$, $V(x)$, $W(x)$ are nonnegative continuous potentials, the nonlinear term $F(x,u,v)=|u|^alpha|v|^beta$ is not 4-superlinear at infinity. Such problem cannot be studied directly by standard variational methods, even by restricting the associated energy functional on the Nehari manifold, because Palais-Smale sequences may not be bounded. Combining some new detailed estimates with truncation technique, we obtain the existence of positive vector solutions for the above system when $b_1+b_2$ small and $lambda$ large. Moreover, the asymptotic behavior of these vector solutions is also explored as $textbf{b}=(b_1,b_2)to bf{0}$ and $lambdatoinfty$. In particular, our results extend some known ones in previous papers that only deals with the case where $4<alpha+beta<6$." @default.
- W3157840812 created "2021-05-10" @default.
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- W3157840812 date "2021-04-24" @default.
- W3157840812 modified "2023-09-23" @default.
- W3157840812 title "Positive solutions for a coupled nonlinear Kirchhoff-type system with vanishing potentials" @default.
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- W3157840812 doi "https://doi.org/10.48550/arxiv.2104.11957" @default.
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