On the existence and behavior of solutions for perturbed nonlinear differential equations
Commun. Korean Math. Soc. 1997 Vol. 12, No. 3, 655-664
Jin Gyo Jeong, Ki-Yeon Shin
Pusan National University, Pusan National University
Abstract : The existence and behavior of a bounded solution for a perturbed nonlinear differential equation of the type $$x'(t)+Ax(t) \ni G(x(t)),\quad t\in [0,\infty)\tag"${\roman {(DE)}}$"$$ is considered. First, we consider the existence of a bounded solution with more simple assumptions using the concept of ``the method of lines". Then we devote to study its behavior using recent results of almost non-expansive curve which is developed by Djafari Rouhani.
Keywords : maximal monotone operator, method of lines, almost nonexpansive curve
MSC numbers : Primary 34K25; Secondary 34K30, 34L20, 47H15
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