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Keywords
(6)
banach fixed point theorem
banach space
Existence and Uniqueness
Mild Solution
Semigroups of Operators
semilinear evolution equations
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Almost automorphic and weighted pseudo almost automorphic solutions of semilinear evolution equations
Almost automorphic and weighted pseudo almost automorphic solutions of semilinear evolution equations,10.1016/j.jfa.2009.06.007,Journal of Functional
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Almost automorphic and weighted pseudo almost automorphic solutions of semilinear evolution equations
(
Citations: 7
)
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Jinghuai Liu
,
Xiaoqiu Song
In this paper, applying the theory of
semigroups of operators
to evolution family and Banach
fixed point
theorem, we prove the
existence and uniqueness
of an (a) almost automorphic (weighted pseudo almost automorphic)
mild solution
of the semilinear
evolution equation
x′(t)=A(t)x(t)+f(t,x(t)) in
Banach space
under conditions.
Journal:
Journal of Functional Analysis  J FUNCT ANAL
, vol. 258, no. 1, pp. 196207, 2010
DOI:
10.1016/j.jfa.2009.06.007
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Citation Context
(1)
...Recently, the existence and uniqueness of pseudo almost automorphic and weighted almost automorphic mild solutions to differential equations in Banach spaces had attracted many researchers[
25
].The automorphic functions have been applied to many areas include physics, mechanics, dynamical system and mathematical biology...
...Next let us recall some basic results about almost automorphy[
25
]...
...Now, from[
5
]Lemma 3.1, we know G(t) is an almost automorphic with respect to t.(i.e.G ∈ AA(R, X).)...
Chouli Lu
,
et al.
Weighted Pseudo Almost Automorphic Solution to a Class of Integrodiffe...
References
(16)
Weighted pseudo almost automorphic functions and applications to abstract differential equations
(
Citations: 8
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J. Blot
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Journal:
Nonlinear Analysistheory Methods & Applications  NONLINEAR ANALTHEOR METH APP
, vol. 71, no. 3, pp. 903909, 2009
Weighted pseudo almost periodic solutions for some partial functional differential equations
(
Citations: 7
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Nadira BoukliHacene
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Khalil Ezzinbi
Journal:
Nonlinear Analysistheory Methods & Applications  NONLINEAR ANALTHEOR METH APP
, vol. 71, no. 9, pp. 36123621, 2009
Weighted pseudo almost periodic functions and applications
(
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Toka Diagana
Journal:
Comptes Rendus Mathematique  C R MATH
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Weighted pseudoalmost periodic solutions to some differential equations
(
Citations: 16
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Toka Diagana
Journal:
Nonlinear Analysistheory Methods & Applications  NONLINEAR ANALTHEOR METH APP
, vol. 68, no. 8, pp. 22502260, 2008
Existence of weighted pseudo almost periodic solutions to some classes of hyperbolic evolution equations
(
Citations: 14
)
Toka Diagana
Journal:
Journal of Mathematical Analysis and Applications  J MATH ANAL APPL
, vol. 350, no. 1, pp. 1828, 2009
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Citations
(7)
Weighted Pseudo Almost Automorphic Solution to a Class of Integrodifferential Equations
Chouli Lu
,
Xiaoqiu Song
,
Lili Zhou
Published in 2011.
Pseudo almost automorphic and weighted pseudo almost automorphic mild solutions to semilinear differential equations in Hilbert spaces
YongKui Chang
,
ZhiHan Zhao
,
Juan J. Nieto
Journal:
Revista Matematica Complutense  REV MAT COMPLUT
, vol. 24, no. 2, pp. 421438, 2011
Pseudo almost automorphic solutions to semilinear differential equations
Jinghuai Liu
Conference:
International Conference on Multimedia Technology  ICMT
, 2011
Almost periodic mild solutions to semilinear fuzzy differential equations
Jinghuai Liu
Conference:
Fuzzy Systems and Knowledge Discovery
, 2011
DoublyWeighted PseudoAlmost Periodic Functions
(
Citations: 1
)
Toka Diagana
Published in 2010.