International Journal of Mathematics and Mathematical Sciences
Volume 9 (1986), Issue 3, Pages 525-530

Continuous dependence of boundary values for semiinfinite interval ordinary differential equations

David H. Eberly

Division of Mathematics, Computer Science, and Systems Design, The University of Texas, San Antonio 78285, Texas, USA

Received 10 December 1985; Revised 8 April 1986

Copyright © 1986 David H. Eberly. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Certain elliptic equations arising in catalysis theory can be transformed into ordinary differential equations on the interval (0,). The solutions to these problems usually depend on parameters ρn, say u(t,ρ). For certain types of nonlinearities, we show that the boundary value u˙(,ρ) is continuous on compact sets of the variable ρ. As a consequence, bifurcation results for the elliptic equation are obtained.