Existência e multiplicidade de soluções de problemas de autovalor não lineares elípticos
Đã lưu trong:
| Tác giả chính: | |
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| Ngày xuất bản: | 2015 |
| Định dạng: | Doctoral thesis |
| Ngôn ngữ: | por |
| Nguồn: | Repositório Institucional da UFG |
| Download full: | http://repositorio.bc.ufg.br/tede/handle/tede/8637 |
Tóm tắt: | In 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). |
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