Solutions of biharmonic equations with mixed nonlinearity. (English) Zbl 1304.35259
Summary: In this paper, we study the following biharmonic equations with mixed nonlinearity: \(\Delta ^2u-\Delta u+V(x)u=f(x,u)+\lambda \xi(x)|u|^{p-2}u\), \(x\in \mathbb R^N\), \(u\in H^2(\mathbb R^N)\), where \(V\in C(\mathbb R^N)\), \(\xi \in L^{\frac{2}{2-p}}(\mathbb R^N)\), \(1\leq p< 2\), and \(\lambda >0\) is a parameter. The existence of multiple solutions is obtained via variational methods. Some recent results are improved and extended.
MSC:
| 35J35 | Variational methods for higher-order elliptic equations |
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