| Abstrakt: |
Abstract: We use the genus theory to prove the existence and multiplicity of solutions for the fractional $p$-Kirchhoff problem $/begin{cases} /displaystyle-\biggl[M /biggl(/int_Q/frac{/vert u(x)-u(y)/vert^p}{/vert x-y /vert^{N+ps}} {/rm d}x {/rm d}y/biggr)/biggr]^{p-1} (-/Delta)_p^su=/lambda h(x,u) /quad/text{in}/ /Omega,// u=0 /quad\text{on}/ /mathbb{R}^N /setminus/Omega, /end{cases} $ where $/Omega$ is an open bounded smooth domain of $/mathbb{R}^N$, $p>1$, $N>ps$ with $s/in(0,1)$ fixed, $Q = /mathbb{R}^{2N}/setminus(C/Omega/times C/Omega)$, $/lambda> 0$ is a numerical parameter, $M$ and $h$ are continuous functions. |
