대한수학회논문집 (Communications of the Korean Mathematical Society)
- 제9권3호
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- Pages.547-564
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- 1994
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- 1225-1763(pISSN)
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- 2234-3024(eISSN)
ON THE COMPACT METHODS FORABSTRACT NONLINEAR FUNCTIONAL EVOLUTION EQUATIONS
- Park, Jong-Yeoul (Department of Mathematics, Pusan National University, Pusan 609-735) ;
- Jung, Jong-Soo (Department of Mathematics, Dong-A University, Pusan 604-714)
- 발행 : 1994.07.01
초록
Let X be a real Banach space. We consider the existence of solutions of the abstract nonlinear functional evolution equation : $$ (E) \frac{du(t)}{dt} + A(t)u(t) + F(u)(t) \ni h(t), $$ $$ u(s) = x_o \in D(A(s)), 0 \leq s \leq t \leq T, $$ where u : $[s, T] \to x$ is an unknown function, ${A(t) : 0 \leq t \leq T}$ is a given family of nonlinear (possibly multivalued) operators in X, and $F : C([s, t];X) \to L^{\infty}([s, X];X)$ and $h : [s, T] \to X$ are given functions.
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