Boundary value problem for certain classes of nonlinear ordinary differential equations with free boundary coercivity (Q2735877)

The author considers the following problem NEWLINE\[NEWLINEm(t) \frac{dV}{dt}= k_1F(t)- f_1(V), \quad -k_2 \frac{dm}{dt}= F(t),\quad f_2(V)+ k_3F(t)= m(t) k_4,NEWLINE\]NEWLINE NEWLINE\[NEWLINE m(0)= M_0, \quad V(0)= V_0, \quad m(t_0)= m_0,NEWLINE\]NEWLINE where \(t\) varies from 0 to \(t_0\), \(f_1 (V)\) and \(f_2 (V)\) are given continuous functions on \(\mathbb{R}_+\), \(k_i\), \(M_0\), \(m_0\), and \(V_0\) are given positive constants, \(m(t)\), \(F(t)\), and \(V(t)\) are unknown functions on the interval \((0, t_0)\). The author proves that this problem is uniquely solvable. The result is used in mathematical modeling of the flight of a winged aircraft along a given trajectory.