This paper is devoted to construction of new solutions to the Cahn-Hilliard equation in ℝd. Staring from the Delaunay unduloid Dô with parameter τ ∈ (0, τ∗) we find for each sufficiently small ε a solution u of this equation ...

Let Sigma be a surface of constant mean curvature in R-3 with multiple Delaunay ends. Assuming that Sigma is non degenerate in this paper we construct new solutions to the Cahn-Hilliard equation epsilon Delta u + epsilon(-1)u(1 ...

We consider an n-dimensional piecewise smooth vector field with two zones separated by a hyperplane σ which admits an invariant hyperplane Ω transversal to σ containing a period annulus A fulfilled by crossing periodic ...

We prove existence of radial positive solutions for the equation

Sea (M, g) una variedad riemanniana cerrada de dimensión n. El problema de Yamabe radica en encontrar una métrica conforme a g con curvatura escalar constante. Se sabe que la respuesta es sı́, y fue probado por Yamabe,Trudinger, ...

We consider the Allen–Cahnequation Δu+u(1−u2)=0inR3. We construct two classes of axially symmetric solutions u=u(|x |,x3)suchthat the (multiple) components of the zero set look for large |x |like catenoids, namely|x3|∼Alog|x ...

En esta tesis doctoral se construyen soluciones rotacionalmente simétricas de la ecuación de Cahn-Hilliard en $ \R{^d} $ y se estudian sus propiedades de estabilidad. En el Capítulo \ref{ch1} se presenta la ecuación de ...