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exponential type of linear nonautonomous
parabolic equations and applications to nonlinear equations
On the boundedness of solutions of the equation
Sufficient conditions on the function $\,f\,$ are given which
boundedness of the solutions of the second order
linear differential equation $\,u''+(1+f(t))\,u=0\,$ as $\, t\rightarrow +\infty\,$.
To do this, a suitable class of quadratic forms is introduced.