POSITIVITY FOR FOURTH-ORDER SEMILINEAR PROBLEMS RELATED TO THE KIRCHHOFF-LOVE FUNCTIONAL

We study the ground states of the following generalization of the Kirchhoff-Love functional, J(sigma)(u) = integral(Omega) (Delta u)(2)/2 - (1 - sigma) integral(Omega) det(del(2)u) - integral(Omega) F(x, u), where Omega is a bounded convex domain in R-2 with C-1,C-1 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 sigma. Positivity of ground states is proved with different techniques according to the range of the parameter sigma is an element of R and we also provide a convergence analysis for the ground states with respect to sigma. Further results concerning positive radial solutions are established when the domain is a ball.