It is known that the antimaximum principle holds for the quasilinear periodic problem (|u′|p−2u′)′ + μ(t) (|u|p−2u) = h(t), u(0) = u(T ), u′(0) = u′(T ), if μ ≥ 0 in [0, T ] and 0 < ‖μ‖∞ ≤ (πp/T ) ,… (More)

We derive existence and approximation results for a type of implicit second order differential equations related with diffusion processes. Singularities, discontinuities and functional dependence are… (More)

Of course, the answer to the question posed in the title is no, in general, but, surprisingly enough, yes in a significant situation to be detailed later. This paper aims to bring to the attention of… (More)

We study the existence of solution for the one-dimensional φ-laplacian equation (φ(u′))′ = λf(t, u, u′) with Dirichlet or mixed boundary conditions. Under general conditions, an explicit estimate λ0… (More)

1 Departamento de Análise Matemática, Facultade de Matemáticas, Campus Sur, Universidade de Santiago de Compostela, 15782 Santiago de Compostela, Spain 2 Departamento de Matemáticas, Universidad de… (More)

In this work, we make an exhaustive study of the properties of the Green’s function related to the periodic boundary value problem Lax ≡ x′′ + a(t) x = 0, x(0) = x(T ), x′(0) = x′(T ), with a… (More)

This paper is devoted to construct an algorithm that allows us to calculate the explicit expression of the Green’s function related to a n – order linear ordinary differential equation, with constant… (More)

We prove the following result: if a continuous vector field F is Lipschitz when restricted to the hypersurfaces determined by a suitable foliation and a transversal condition is satisfied at the… (More)

We study the existence of extremal solutions for an infinite system of first-order discontinuous functional differential equations in the Banach space of the bounded functions l∞.M/. 2000Mathematics… (More)