Positive Solutions of Schrödinger Equations in Two-Dimensional Exterior Domains.
Geometrical methods in hydrodynamics
We describe some recent results on a specific nonlinear hydrodynamical problem where the geometric approach gives insight into a variety of aspects.
Existence of permanent and breaking waves for a shallow water equation : a geometric approach
The existence of global solutions and the phenomenon of blow-up of a solution in finite time for a recently derived shallow water equation are studied. We prove that the only way a classical solution could blow-up is as a breaking wave for which we determine the exact blow-up rate and, in some cases, the blow-up set. Using the correspondence between the shallow water equation and the geodesic flow on the manifold of diffeomorphisms of the line endowed with a weak Riemannian structure, we give sufficient...
A general-weighted Sturm-Liouville problem
Sur un problème aux limites de la théorie du transfert de masse et de chaleur
A Gronwall-like inequality and its applications
A generalized Gronwall-like inequality is established and applied in obtaining a right saturated solution for a class of differential equations and in estimating the solution of an evolution equation for the so called hidden variables.
Some observations on a Conti's result
An extension of a result of R. Conti is given from which some integro-differential inequalities of the Gronwall-Bellman-Bihari type and a criterion for the continuation of solutions of a system of ordinary differential equations are deduced.
On the existence, uniqueness and parametric dependence on the coefficients of the solution processes in McShane's stochastic integral equations.
In this paper we use the Schauder fixed point theorem and methods of integral inequalities in order to prove a result on the existence, uniqueness and parametric dependence on the coefficients of the solution processes in McShane stochastic integral equations.
Global existence and blow-up for a shallow water equation
Positive solutions of elliptic equations in two-dimensional exterior domains.
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