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Existence and concentration for Kirchhoff type equations around topologically critical points of the potential

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  • We consider the existence and concentration of solutions for the following Kirchhoff Type Equations

    $-\varepsilon^2 M \left( \varepsilon^{2-N} \displaystyle \int_{\mathbb{R}^N} |\nabla v|^2dx \right)Δ v+V(x)v=f(v), \mathrm{in} \ \mathbb{R}^N.$

    Under suitable conditions on the continuous functions $M$, $V$ and $f$, we obtain a family of positive solutions concentrating around the local maximum or saddle points of $V$. Moreover with appropriate assumptions on $V$, we also have multiple solutions clustering respectively around three kinds of critical points of $V$.

    Mathematics Subject Classification: 35B05, 35B45.

    Citation:

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