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- W4313489920 abstract "<abstract><p>In this paper, we consider the following nonlinear Kirchhoff-type problem with sublinear perturbation and steep potential well</p> <p><disp-formula> <label/> <tex-math id=FE1> begin{document}$ begin{eqnarray*} left {begin{array}{ll} -Big(a+bint_{mathbb{R}^3}|nabla u|^2dxBig)Delta u+lambda V(x)u = f(x,u)+g(x)|u|^{q-2}u mbox{in} mathbb{R}^3, uin H^1(mathbb{R}^3), end{array} right. label{1} end{eqnarray*} $end{document} </tex-math></disp-formula></p> <p>where $ a $ and $ b $ are positive constants, $ lambda > 0 $ is a parameter, $ 1 < q < 2 $, the potential $ Vin C(mathbb{R}^3, mathbb{R}) $ and $ V^{-1}(0) $ has a nonempty interior. The functions $ f $ and $ g $ are assumed to obey a certain set of conditions. The existence of two nontrivial solutions are obtained by using variational methods. Furthermore, the concentration behavior of solutions as $ lambdarightarrow infty $ is also explored.</p></abstract>" @default.
- W4313489920 created "2023-01-06" @default.
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- W4313489920 date "2023-01-01" @default.
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- W4313489920 title "Existence and concentration of solutions for a Kirchhoff-type problem with sublinear perturbation and steep potential well" @default.
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- W4313489920 doi "https://doi.org/10.3934/math.2023325" @default.
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