Global solutions for abstract differential equations with state dependent delay

• Grant number: 17/13145-8
• Support Opportunities: Regular Research Grants
• Start date: September 01, 2017
• End date: August 31, 2019
• Field of knowledge: Physical Sciences and Mathematics - Mathematics - Analysis
• Principal Investigator: Eduardo Alex Hernández Morales
• Grantee: Eduardo Alex Hernández Morales
• Host Institution: Faculdade de Filosofia, Ciências e Letras de Ribeirão Preto (FFCLRP). Universidade de São Paulo (USP). Ribeirão Preto , SP, Brazil

Abstract

The objective of this project is the study of the existence and the qualitative properties of solutions of differential equations with state-dependent delay. In particular, we will study the existence of global solutions for abstract neutral differential equations with state dependent delay and traveling waves solutions for partial differential equations with state dependent delay. This project allows us to continue our research activities associated to the postdoctoral fellowship “Traveling wave for partial neutral functional differential equations", (FAPEPs: 2014/25818-9), developed at York University, Toronto, Canada, (August 2015-July 2016) with the colaboration of Jianhong Wu. This Project consider also research activities with Sergei Trofimchuk, from Talca University, Chile. (AU)

Scientific publications

(7)

(References retrieved automatically from Web of Science and SciELO through information on FAPESP grants and their corresponding numbers as mentioned in the publications by the authors)

HERNANDEZ, EDUARDO. Existence and uniqueness of global solution for abstract second order differential equations with state-dependent delay. Mathematische Nachrichten, v. 295, n. 1, p. 124-139, JAN 2022. (17/13145-8)

HERNANDEZ, EDUARDO; TROFIMCHUK, SERGEI. Traveling waves solutions for partial neutral differential equations. Journal of Mathematical Analysis and Applications, v. 481, n. 1, JAN 1 2020. (17/13145-8, 18/06658-1)

HERNANDEZ, EDUARDO. On abstract differential equations with state dependent non-local conditions. Journal of Mathematical Analysis and Applications, v. 466, n. 1, p. 408-425, OCT 1 2018. (17/13145-8)

HERNANDEZ, EDUARDO; TROFIMCHUK, SERGEI. Nonstandard Quasi-monotonicity: An Application to the Wave Existence in a Neutral KPP-Fisher Equation. Journal of Dynamics and Differential Equations, v. 32, n. 2, p. 921-939, JUN 2020. (17/13145-8, 18/06658-1)

HERNANDEZ, EDUARDO; PIERRI, MICHELLI. S-ASYMPTOTICALLY PERIODIC SOLUTIONS FOR ABSTRACT EQUATIONS WITH STATE-DEPENDENT DELAY. BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY, v. 98, n. 3, p. 456-464, DEC 2018. (17/13145-8)

HERNANDEZ, EDUARDO. Existence and uniqueness of global solution for abstract second order differential equations with state-dependent delay. Mathematische Nachrichten, v. 295, n. 1, JAN 2022. (17/13145-8)

HERNANDEZ, EDUARDO; WU, JIANHONG. EXISTENCE, UNIQUENESS AND QUALITATIVE PROPERTIES OF GLOBAL SOLUTIONS OF ABSTRACT DIFFERENTIAL EQUATIONS WITH STATE-DEPENDENT DELAY. PROCEEDINGS OF THE EDINBURGH MATHEMATICAL SOCIETY, v. 62, n. 3, p. 771-788, AUG 2019. (17/13145-8)