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A two-point Neumann boundary value problem for a two ion electro-diffusion model reducible to the Painlevé II equation is investigated. The problem is unconventional in that the model equation involves yet-to-be determined boundary values of the solution. In prior work by Thompson, the existence of a solution was established subject to an inequality on the physical parameters. Here, a two-dimensional shooting method is used to show that this restriction may be removed. A practical algorithm for the solution of the boundary value problem is presented in an appendix Fil: Amster, Pablo Gustavo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina Fil: Kwong, M. K.. Hong Kong Polytechnic University; China Fil: Rogers, C.. University Of New South Wales; Australia

This work deals with the existence and symmetry of positive solutions for a Neumann boundary value problem. It is a generalization of the work of Pedro J. Torres. The main result is the uniqueness of positive solutions, which is proved by an analytical method, for a given interval of the positive parameter q.

A time-optimal control problem for linear infinite order distributed parabolic systems involving constant time lags appear both in the state equation and in the boundary condition is presented. Some particular properties of the optimal control are discussed.

We study a Neumann problem for a nonlinear elliptic system. Unlike previous results in the literature of Landesman–Lazer type, our existence theorem allows rapid rotations on the nonlinear term. Fil: Amster, Pablo Gustavo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina Fil: Clapp, Mónica. Universidad Nacional Autónoma de México; México Fil: Haddad, Julián Eduardo. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Departamento de Matemática; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina