Existence of a positive solution and numerical solution for some elliptic superlinear problem |
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| Authors: | D.L. Cecílio C. Cuevas J.G. Mesquita P. Ubilla |
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| Affiliation: | 1. Universidade de São Paulo, Engenharia de Estruturas, Avenida Trabalhador São Carlense, 400, 13566-590, São Carlos, SP, Brazil;2. Universidade Federal de Pernambuco, Departamento de Matemática, Av. Jornalista Aníbal Fernandes, sn, Cidade Universitária, 50740-560, Recife, PE, Brazil;3. Universidade de Brasília, Departamento de Matemática, Campus Universitário Darcy Ribeiro, Asa Norte, 70910-900, Brasília, DF, Brazil;4. Universidad de Santiago de Chile, Facultad de Ciencia, Departamento de Matemática y Ciencia de la Computación, Casilla 307, Correo 2, Santiago, Chile |
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| 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. |
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| Keywords: | Corresponding author. |
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