| Full text | |
| Author(s): |
dos Santos, Ederson Moreira
;
Pacella, Filomena
Total Authors: 2
|
| Document type: | Journal article |
| Source: | COMMUNICATIONS IN CONTEMPORARY MATHEMATICS; v. 19, n. 3 JUN 2017. |
| Web of Science Citations: | 3 |
| Abstract | |
We consider non- autonomous semilinear elliptic equations of the type -triangle u = |x|(alpha)f(u), x epsilon Omega, u= 0 on partial derivative Omega, where Omega subset of R-2 is either a ball or an annulus centered at the origin, alpha > 0 and f : R -> R is C-1,C-beta on bounded sets of R. We address the question of estimating the Morse index m(u) of a sign changing radial solution u. We prove that m(u) >= 3 for every alpha > 0 and that m(u) >= alpha + 3 if alpha is even. If f is superlinear the previous estimates become m(u) >= n(u) + 2 and m(u) >= alpha + n(u) + 2, respectively, where n(u) denotes the number of nodal sets of u, i. e. of connected components of [x epsilon Omega; u(x) not equal 0]. Consequently, every least energy nodal solution u(alpha) is not radially symmetric and m(u(alpha)) -> +infinity as alpha -> +infinity along the sequence of even exponents alpha. (AU) | |
| FAPESP's process: | 14/03805-2 - Nonlinear elliptic partial differential equations and systems |
| Grantee: | Ederson Moreira dos Santos |
| Support Opportunities: | Scholarships abroad - Research |