Abstract
The paper discusses the solvability of the singular Dirichlet boundary value problem u 00 .t/C a t u 0 .t/ a t2 u.t/Df.t;u.t/;u 0 .t//; u.0/D0; u.T/D0: Here a 2 .1 ; 1/ and f satisfies the local Caratheodory conditions on a0;Tc D, where D D.0;1/ R. It is shown that the cardinality of the set L of all positive solutions to the problem is a continuum. In addition, the structure and properties of the set L are described. Applications and numerical simulations of the results are presented.
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