Multiple nontrivial solutions for a nonlocal problem with sublinear nonlinearity (Q2244311)

Summary: In this paper, we study the following nonlocal problem \[ \begin{cases} -(a-b\int_\Omega |\nabla u|^2 d x) \varDelta u = \lambda u + f (x)|u|^{p - 2} u , & x \in \Omega ,\\ u = 0, & x \in \partial \Omega, \end{cases} \] where \(a,b>0\) are constants, \(1<p<2\), \(\lambda>0\), \(f\in L^\infty(\Omega)\) is a positive function, and \(\Omega\) is a smooth bounded domain in \(\mathbb{R}^N\) with \(N\geq3\). By variational methods, we obtain a pair of nontrivial solutions for the considered problem provided \(|f|_\infty\) is small enough.