Existence of solutions to biharmonic equations with sign-changing coefficients
Somayeh Saiedinezhad · DOAJ (DOAJ: Directory of Open Access Journals) · 2018
In this article, we study the existence of solutions for the semi-linear elliptic equation $$ \Delta^2 u-a(x)\Delta u=b(x)| u|^{p-2}u $$ with Navier boundary condition $u=\Delta u=0$ on $\partial\Omega$, where $\Omega$ is a bounded domain with smooth boundary and $2<p<2^*$. We consider two different assumptions on the potentials $a$ and $b$, including the case of sign-changing weights. The approach is based on the Nehari manifold with variational arguments about the corresponding fibering map, which ensures the multiple results.