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

where $Ω$ is a bounded convex domain in $ℝ^{2}$ with $C^{1, 1}$ 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 $σ$ . Positivity of ground states is proved with different techniques according to the range of the parameter $σ \in ℝ$ and we also provide a convergence analysis for the ground states with respect to $σ$ . Further results concerning positive radial solutions are established when the domain is a ball.

Keywords

biharmonic operator, positivity-preserving property, semilinear problem, positive least-energy solutions, Nehari manifold

Mathematical Subject Classification 2010

Primary: 35G30, 49J40

Milestones

Received: 29 June 2016

Revised: 6 February 2017

Accepted: 7 March 2017

Published: 9 May 2017

Authors

Giulio Romani
Aix Marseille Univ, CNRS, Centrale Marseille Institute de Mathématique de Marseille (I2M) 13453 Marseille France

Vol. 10, No. 4, 2017

Giulio Romani

Abstract

Keywords

Mathematical Subject Classification 2010

Milestones

Authors