We study the ground states of the following generalization of the Kirchhoff–Love functional,
where is a bounded convex domain in with boundary and the nonlinearities involved are of sublinear type or superlinear with power growth. These critical points correspond to least-energy weak solutions to a fourth-order semilinear boundary value problem with Steklov boundary conditions depending on . Positivity of ground states is proved with different techniques according to the range of the parameter and we also provide a convergence analysis for the ground states with respect to . Further results concerning positive radial solutions are established when the domain is a ball.
"Positivity for fourth-order semilinear problems related to the Kirchhoff–Love functional." Anal. PDE 10 (4) 943 - 982, 2017. https://doi.org/10.2140/apde.2017.10.943