Positivity for fourth-order semilinear problems related to the Kirchhoff-Love functional

Giulio Romani

We study the ground states of the following generalization of the Kirchhoff-Love functional, $$J_{\sigma }(u)={\int }_{\Omega }\frac{(\Delta u{)}^2}{2}-(1-\sigma ){\int }_{\Omega }det({\nabla }^{2}u)-{\int }_{\Omega }F(x,u),$$ where $\Omega$…