A note on nonlinear fourth-order elliptic equations on $$\mathbb R ^N$$

Lin Li () and Wen-Wu Pan ()

Journal of Global Optimization, 2013, vol. 57, issue 4, 1319-1325

Abstract: We established the existence of weak solutions of the fourth-order elliptic equation of the form $$\begin{aligned} \Delta ^2 u -\Delta u + a(x)u=\lambda b(x) f(u) + \mu g (x, u), \qquad x \in \mathbb{R }^N, u \in H^2(\mathbb{R }^N), \end{aligned}$$ where $$\lambda $$ is a positive parameter, $$a(x)$$ and $$b(x)$$ are positive functions, while $$f : \mathbb{R }\rightarrow \mathbb{R }$$ is sublinear at infinity and superlinear at the origin. In particular, by using Ricceri’s recent three critical points theorem, we show that the problem has at least three solutions. Copyright Springer Science+Business Media New York 2013

Keywords: Multiple solutions; Three critical points theorem; Nonlinear fourth-order elliptic equations; Variational method; Primary: 35J35; Secondary: 47J10; 35J91; 58E05 (search for similar items in EconPapers)
Date: 2013
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DOI: 10.1007/s10898-012-0031-0

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