A note about positive solutions for an equation of Kirchhoff type

Multiple Solutions for an Equation of Kirchhoff Type: Theoretical and Numerical Aspects

“…In most studies, numerical solutions are obtained by fixed point methods, according to [12]. More specifically, an iterative sequence based on operator given by equation (2.1) define the method.…”

“…Additional tests are run by using an algorithm based on the Banach Fixed Point Theorem. Considering some hypothesis about the functions f and M, we can demonstrate, using the Banach Fixed Point Theorem (details in [12]), the local convergence of algorithms that use the iterative sequence u k+1 = T (u k ).…”

“…For a wide spectrum of study, we recommend [2], [3], [6], [10] and more recently [5]. Concerning the problem (1.1) we can observe by [12] that studies with theoretical aspects were developed using Banach's Fixed Point Theorem or Leray-Schauder Alternative combined with Krasnoselskii's Theorem. Consequently, it is natural to ask about existence results by using Avery-Peterson Theorem [4].…”

Uso do teorema de ponto fixo de Banach para a determinação de solução de uma Equação do tipo de Kirchhoff

“…Vamos determinar solução para (1) baseado nos resultados apresentados em [2], trabalharemos no espaço…”

“…Este estudo encontra-se em fase inicial e pretendemos além de explorar os resultados teóricos fornecidos pelo Teorema de Ponto Fixo de Banach vamos também realizar testes numéricos com algoritmos baseados na sequencia iterativa definida em (2). Palavras-chave: Equação de Kirchhoff, Ponto fixo, Teorema de Banach…”