The existence of nontrivial solution for a class of sublinear biharmonic equations with steep potential well

In this paper, we study the following biharmonic equation: $$ \textstyle\begin{cases} \Delta^{2}u - \Delta u + \lambda V( x)u = \alpha( x) f(u) + \mu K(x) \vert u \vert ^{q-2}u \quad\text{in } \mathbb{R}^{N},\\ u\in H^{2}(\mathbb{R}^{N}), \end{cases} $$ where $\Delta^{2}u=\Delta(\Delta u)$ , $N>4$ , $\lambda>0$ , $1< q<2$ and $\mu\in[0,\mu_{0}]$ . By using Ekeland’s variational principle and Gigliardo–Nirenberg’s inequality, we prove the existence of nontrivial solution for the above problem.

Abstract licence: CC BY-NC-ND

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