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| Three Solutions for a Perturbed Integral Equation with Homogeneous Dirichlet Condition |
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| KeyWord:Integral elliptic equation, variational methods, critical points |
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| Abstract: |
| We consider the integral equation
$-\mathcal{L}^p_K u
=\lambda f(x,u)+\mu g(x,u)$,
with homogeneous Dirichlet condition on a bounded Lipschitz domain of $\mathbb{R}^N$ where $\lambda,\mu\in \real$,
$p\geq 2$, $s\in]0,1[$, $N>ps$, $f,g:\Real\longrightarrow \real$ are Carath\'eodory functions with subcritical growth and $-\mathcal{L}^p$ denotes a class of operators that includes $(-\Delta)^s_p$, the fractional $p$-Laplacian. Here $\mu g$ represents a small perturbation of $\lambda f$. Applying an abstract critical point theorem due to Ricceri, a variational setting developed by Xiang et al. and a Minti-Browder's theorem, we prove the existence of three weak solutions. |
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