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On a continuous method for solving nonlinear operator equations
Differential Equations, 2012The article deals with solutions to a nonlinear operator equation \[ A(x) - f = 0\tag{1} \] with a Fréchet or Gâteaux differentiable nonlinear operator \(A(x)\) and to the Cauchy problem \[ \frac{dx(t)}{dt} = A(x(t)) - f, \quad x(0) = x_0.\tag{2} \] The author, in terms of the logarithmic norm of the operators \(A'(x)\), formulates conditions under ...
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