Injetividade do Funcional Dirichlet-Neumann Elítico via Matemática Intervalar
DOI:
https://doi.org/10.5540/tema.2009.010.01.0031Abstract
O estudo da injetividade do Funcional Dirichlet-Neumann Elítico, no anel de raios 1 e 2, está condicionado à existência de uma única solução, de período 2, para a equação (e²y − 1)λ = 2y′′ − (y′)2, onde λ é uma função que só depende de r > 1, raio externo do anel Ar. Se λ ≥ 0 mostra-se que a única solução dessa equação é y = 0 para a condição inicial y(0) = 0; para λ < 0 também é possível encontrar as soluções. O objetivo deste trabalho é estudar, usando a matemática intervalar, para que valores de r > 1, a função λ é positiva, nula ou negativa. Como conclusões do mesmo, constatou-se que a função λ é não negativa para 1 < r ≤ 4,9202261876221005, e negativa para r ≥ 4, 9202261876221014.References
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