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Sign-changing multi-bump solutions for Kirchhoff-type equations in $\mathbb{R}^3$

  • * Corresponding author: Wei Shuai

    * Corresponding author: Wei Shuai
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  • We are interested in the existence of sign-changing multi-bump solutions for the following Kirchhoff equation

    $ - (a + b\int_{{\mathbb{R}^3}} {|\nabla u{|^2}dx} )\Delta u + \lambda V(x)u = f(u),\;x \in {\mathbb{R}^3},$

    where $λ$>0 is a parameter and the potential $V(x)$ is a nonnegative continuous function with a potential well $Ω: = int(V^{-1}(0))$ which possesses $k$ disjoint bounded components $Ω_1,Ω_2,···,Ω_k$. Under some conditions imposed on $f(u)$, multiple sign-changing multi-bump solutions are obtained. Moreover, the concentration behavior of these solutions as $λ→ +∞$ are also studied.

    Mathematics Subject Classification: Primary: 35J60, 35J20; Secondary: 35J01, 35J40.


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