January/February 2024 Concavity properties for quasilinear equations and optimality remarks
Nouf M. Almousa, Jacopo Assettini, Marco Gallo, Marco Squassina
Differential Integral Equations 37(1/2): 1-26 (January/February 2024). DOI: 10.57262/die037-0102-1

Abstract

In this paper, we study quasiconcavity properties of solutions of Dirichlet problems related to modified nonlinear Schrödinger equations of the type$$-{\rm div}\big(a(u) \nabla u\big) + \frac{a'(u)}{2} |\nabla u|^2 = f(u) \quad \hbox{in $\Omega$},$$where $\Omega$ is a convex bounded domain of $\mathbb{R}^N$.In particular, we search for a function $\varphi:\mathbb{R} \to \mathbb{R}$, modeled on $f\in C^1$ and $a\in C^1$, which makes $\varphi(u)$ concave. Moreover, we discuss the optimality of the conditions assumed on the source.

Citation

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Nouf M. Almousa. Jacopo Assettini. Marco Gallo. Marco Squassina. "Concavity properties for quasilinear equations and optimality remarks." Differential Integral Equations 37 (1/2) 1 - 26, January/February 2024. https://doi.org/10.57262/die037-0102-1

Information

Published: January/February 2024
First available in Project Euclid: 20 September 2023

Digital Object Identifier: 10.57262/die037-0102-1

Subjects:
Primary: 26B25 , 35B99 , 35E10 , 35J60 , 35J62

Rights: Copyright © 2024 Khayyam Publishing, Inc.

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Vol.37 • No. 1/2 • January/February 2024
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