Analysis & PDE
- Anal. PDE
- Volume 10, Number 4 (2017), 943-982.
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,
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.
Anal. PDE, Volume 10, Number 4 (2017), 943-982.
Received: 29 June 2016
Revised: 6 February 2017
Accepted: 7 March 2017
First available in Project Euclid: 19 October 2017
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Romani, Giulio. Positivity for fourth-order semilinear problems related to the Kirchhoff–Love functional. Anal. PDE 10 (2017), no. 4, 943--982. doi:10.2140/apde.2017.10.943. https://projecteuclid.org/euclid.apde/1508432243