Low perturbations and combined effects of critical and singular nonlinearities in Kirchhoff problems
Given a bounded domain \(\Omega \subset \mathbb{R}^3\) with smooth boundary \(\partial\Omega\), this paper is concerned with Kirchhoff problems involving critical growth and singular terms given by \[ \begin{cases} -\left(a+b\displaystyle \int_\Omega |\nabla u|^2\,\mathrm{d}x\right)\Delta u=\lambda u^{-\gamma}+u^5,\quad &\text{in }\Omega,\\ u>0&\text{in }\Omega,\\ u=0,&\text{on }\partial\Omega, \end{cases} \] where \(\gamma \in (0,1)\), \(a\), \(b\) are positive constants, \(\lambda>0\) is a parameter and \(\Delta\) denotes the Laplacian. Applying variational methods, the authors prove the existence of at least two positive solutions provided the parameter \(\lambda>0\) is sufficiently small.
scientific article; zbMATH DE number 7615105
scientific article