https://revistaschilenas.uchile.cl/handle/2250/42131 \([0-9]{4}\) 2026-08-02T21:49:22Z https://revistaschilenas.uchile.cl/handle/2250/255904 A nonresonance between non-consecutive eigenvalues of semilinear elliptic equations : Variational methods We study the solvability of the problem ??u = f(x, u) + h in ? ; u = 0 on ??when the nonlinearity f is assumed to lie asymptotically between two non- consecutive eigenvalues of ??. We show that this problem is nonresonant. https://revistaschilenas.uchile.cl/handle/2250/255902 A multiplier gliding hump property for sequence spaces We consider the Banach-Mackey property for pairs of vector spaces E and E0 which are in duality. Let A be an algebra of sets and assume that P is an additive map from A into the projection operators on E. We define a continuous gliding hump property for the map P and show that pairs with this gliding hump property and another measure theoretic property are Banach-Mackey pairs,i.e., weakly bounded subsets of E are strongly bounded. Examples of vector valued function spaces, such as the space of Pettis integrable functions, which satisfy these conditions are given. https://revistaschilenas.uchile.cl/handle/2250/255903 Nonlinear elliptic problems with resonance at the two first eigenvalue : A variational approach We study the nonlinear elliptic problems with Dirichlet boundary condition {-Dpu=¦(x, u) in Wu=0 on ¶W Resonance conditions at the first or at the second eigenvalue will be considered.   https://revistaschilenas.uchile.cl/handle/2250/255901 Conjugacies classes of some numerical methods We study the dynamics of some numerical root finding methods such as the Newton, Halley, K¨onig and Schröder methods for three and four degree complex polynomials.