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On a \(p\)-Kirchhoff equation via Krasnoselskii’s genus. (English) Zbl 1171.35371

Summary: In this work will use the genus theory, introduced by Krasnoselskii, to show a result of existence and multiplicity of solutions of the \(p\)-Kirchhoff equation
\[ -\left[M\left(\int_\Omega |\nabla u|^p\,dx\right)\right]^{p-1}\Delta_pu=f(x,u) \text{ in }\Omega,\quad u=0\text{ on }\partial\Omega \]
where \(\Omega\) is a bounded smooth domain of \(\mathbb R^N\), \(1<p<N\), and \(M\) and \(f\) are continuous functions.

MSC:

35J60 Nonlinear elliptic equations
35D05 Existence of generalized solutions of PDE (MSC2000)
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References:

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