Doutorado em Matemática (IME)
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Navegando Doutorado em Matemática (IME) por Assunto "Autovalores"
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Item Existência e multiplicidade de soluções de problemas de autovalor não lineares elípticos(Universidade Federal de Goiás, 2015-07-03) Silva, Kaye Oliveira da; Gonçalves, José Valdo Abreu; http://buscatextual.cnpq.br/buscatextual/visualizacv.do?id=K4781975P5; Gonçalves, José Valdo Abreu; Correa, Francisco Julio Sobreira de Araujo; Rodrigues, Rodrigo da Silva; Mota, Jesus Carlos da; Silva, Edcarlos Domingos daIn this work, we study two problems in partial differential equations. The first one is a nonlinear eigenvalue problem given by: ( div( (jruj)ru) = f(x; u) em , u = 0 em @ , where the nonlinearity f is oscilatory. By using Orlicz-Sobolev spaces and techniques of minimization, degree theory, lower and upper solutions and regularization of solutions, we show that for each sufficiently big, there is a family of solutions, which is finite when f oscillates a finite number of times (with respect to the second variable) and it is infinite when f oscillates infinitely many times. On the second problem, we use the shooting method, to show that the problem: ( (r (ju0(r)j)u0(r))0 = r f(u(r)); 0 < r < R; u(R) = u0(0) = 0; has for each sufficiently small, a family fukg1k =1 of solutions, where for each positive integer k, uk has exactly k roots in the interval (0;R).