Abstract
This paper is dedicated to investigating the following fourth-order elliptic equation with Kirchhoff-type \[ \begin{cases} \displaystyle \Delta^{2} u - \left( a + b \int_{\mathbb{R}^{N}} |\nabla u|^{2} \, dx \right) \Delta u + cu = f(u) &\textrm{in $\mathbb{R}^{N}$}, \\ u \in H^{2}(\mathbb{R}^{N}), \end{cases} \] where $a \gt 0$, $b \geq 0$ and $c \gt 0$ are constants. By using cut-off functional and monotonicity tricks, we prove that the above problem has a positive solution. Our result cover the case where the nonlinearity satisfies asymptotically linear and superlinear condition at the infinity, which extend the results of related literatures.
Citation
Jianping Huang. Qi Zhang. "Existence of Nonnegative Solutions for Fourth Order Elliptic Equations of Kirchhoff Type with General Subcritical Growth." Taiwanese J. Math. 24 (1) 81 - 96, February, 2020. https://doi.org/10.11650/tjm/190202
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