Three solutions for parametric problems with nonhomogeneous \((a,2)\)-type differential operators and reaction terms sublinear at zero (Q2325927)

The authors study the following parametric Dirichlet problem \[ \begin{cases} -\text{div\,}a(\nabla u)-\Delta u =f_\lambda (x,u) & \text{in } \Omega,\\ u \big |_{\partial\Omega}, \end{cases} \] where \(\Omega\subseteq \mathbb{R}^N\) is a bounded domain with a \(C^{2,\alpha}\)-boundary \(\partial\Omega\), \(0<\alpha \leq 1\), \(-\text{div\,}a(\nabla \cdot)\) is a nonhomogeneous operator and the right-hand side is a Carathéodory function which depends on the parameter \(\lambda>0\). The authors prove the existence of three distinct nontrivial smooth solutions for small values of the parameter and all of them have sign information: one is positive, one is negative and the third one is nodal.