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- 한국산업응용수학회 JOURNAL OF THE KOREAN SOCIETY FOR INDUSTRIAL AND APPLIED MATHEMATICS Journal of the Korean Society for Industrial and Applied Mathematics Vol.13 No.3
- 발행연도
- 2009.8
- 수록면
- 203 - 215 (13page)
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In this article, we study the existence and uniqueness of mild and classical solutions for a nonlinear impulsive differential equation with nonlocal conditions
u'(t) = Au(t) + f(t, u(t), Tu(t), Su(t)), 0 ≤ t ≤ T?, t ≠ t<SUB>i</SUB>,
u(0) + g(u) = uu(0) + g(u) = u?,
△u(t<SUB>i</SUB>) = I<SUB>i</SUB>(u(t<SUB>i</SUB>)), i = 1, 2,... p, 0 ＜ t₁ ＜ t₂ ＜ … ＜ t<SUB>p</SUB> ＜ T?,
in a Banach space X, where A is the infinitesimal generator of a C? semigroup, g constitutes a nonlocal conditions, and △u(t<SUB>i</SUB>) = u(t?<SUB>i</SUB> ) - u(t?<SUB>i</SUB> ) represents an impulsive conditions.
u'(t) = Au(t) + f(t, u(t), Tu(t), Su(t)), 0 ≤ t ≤ T?, t ≠ t<SUB>i</SUB>,
u(0) + g(u) = uu(0) + g(u) = u?,
△u(t<SUB>i</SUB>) = I<SUB>i</SUB>(u(t<SUB>i</SUB>)), i = 1, 2,... p, 0 ＜ t₁ ＜ t₂ ＜ … ＜ t<SUB>p</SUB> ＜ T?,
in a Banach space X, where A is the infinitesimal generator of a C? semigroup, g constitutes a nonlocal conditions, and △u(t<SUB>i</SUB>) = u(t?<SUB>i</SUB> ) - u(t?<SUB>i</SUB> ) represents an impulsive conditions.
목차
ABSTRACT
1. INTRODUCTION
2. EXISTENCE RESULTS
ACKNOWLEDGEMENTS
REFERENCES
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UCI(KEPA) : I410-ECN-0101-2009-410-018856356