Tekil diferansiyel denklemlerin çözümleri üzerine

ABSTRACT The question of existence and uniqueness of solutions to singular nonlinear two-point boundary value problems is of fundamental importance. In this thesis existence and uniqueness of solutions to a mixed problem are established and a nonlinear model is developed and is solved approximately as an application to the theory. Existence and uniqueness results are obtained for the mixed boundary value problem P(t) (p(t)y'(t))' + f{t,y{t),p(t)y'{t)) = 0, 0 < t < 1 lim/7(0/(0 = 0, XI) = 0 t->0+ limf(t,y,py') = co with f : [0,1] x (0,oo) x (-00,00) -> (0,oo) continuous and peC[0,l]nC'(0,l] with p > 0 on (0,1), p(0) = 0 and J dt = 00 A mathematical model is improved for the temperature distribution in the human head by assuming that the thermal conductivity k is not a constant but a function of temperature T. Numerical solutions are obtained for this model by the finite difference method and are compared with some others results.