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2017 Positivity for fourth-order semilinear problems related to the Kirchhoff–Love functional
Giulio Romani
Anal. PDE 10(4): 943-982 (2017). DOI: 10.2140/apde.2017.10.943

Abstract

We study the ground states of the following generalization of the Kirchhoff–Love functional,

Jσ(u) =Ω(Δu)2 2 (1 σ)Ω det(2u) ΩF(x,u),

where Ω is a bounded convex domain in 2 with C1,1 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 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.

Citation

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Giulio Romani. "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

Information

Received: 29 June 2016; Revised: 6 February 2017; Accepted: 7 March 2017; Published: 2017
First available in Project Euclid: 19 October 2017

zbMATH: 06715608
MathSciNet: MR3649372
Digital Object Identifier: 10.2140/apde.2017.10.943

Subjects:
Primary: 35G30, 49J40

Rights: Copyright © 2017 Mathematical Sciences Publishers

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