Existence of a positive solution and numerical solution for some elliptic superlinear problem

Author(s)

Cecilio, D. L. ^[1] ; Cuevas, C. ^[2] ; Mesquita, J. G. ^[3] ; Ubilla, P. ^[4]

Affiliation

^[1] Univ Sao Paulo, Engn Estruturas, Ave Trabalhador Sao Carlense 400, BR-13566590 Sao Carlos, SP - Brazil

^[2] Univ Fed Pernambuco, Dept Matemat, Av Jornalista Anibal Fernandes SN, BR-50740560 Recife, PE - Brazil

^[3] Univ Brasilia, Dept Matemat, Campus Univ Darcy Ribeiro, BR-70910900 Brasilia, DF - Brazil

^[4] Univ Santiago Chile, Fac Ciencia, Dept Matemat & Ciencia Computac, Casilla 307, Correo 2, Santiago - Chile

• Document type: Journal article
• Source: Journal of Differential Equations; v. 266, n. 2-3, p. 1338-1356, JAN 15 2019.
• Web of Science Citations: 0

Abstract

In this paper, we prove the existence of positive solutions of an elliptic superlinear problem. Also, we are interested here in getting results concerning the existence of positive solutions for the discrete formulation of our problem. Therefore, in order to do it, we employ the radial solutions of the elliptic superlinear problem, obtaining a second-order dynamic equation on time scales, which encompasses discrete, continuous and hybrid formulations of our problem. This unified equation allows us to present numerical simulations, which give us a more precise analysis and description concerning the behavior of the solution according to the parameters. (C) 2018 Elsevier Inc. All rights reserved. (AU)

• FAPESP's process: 13/17104-3 - Impulsive functional dynamic equations on time scales and applications
• Grantee: Jaqueline Godoy Mesquita
• Support Opportunities: Research Grants - Young Investigators Grants