| Abstract: | The paper deals with several problems having the following common feature. The differential equation under consideration contains
a power function of the solution or of its gradient, with the exponent depending on a small parameter. This dependence is
such that a certain property of the solutions corresponding to the positive values of the parameter may disappear as the latter
tends to zero. This phenomenon is shown to be lacking in the case where not only the said exponent, but also the coefficients
of the equation depend on the small parameter in a suitable way. Several theorems are proved on sharp conditions, ensuring
such uniformity of various properties exhibited by the solutions. Bibliography: 44 titles.
Dedicated to Olga Arsenievna Oleinik
This paper has been supported in part by the Russian Foundation for Basic Research (Project 93-013-1744) and by the International
Science Foundation (Grant MIE000).
Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 19, pp. 000-000, 0000. |
