zbMATH — the first resource for mathematics

Examples
Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Semilinear evolution inclusions with nonlocal conditions. (English) Zbl 1173.34338
Summary: We discuss conditions for the existence of at least one solution of semilinear evolution inclusions with a nonlocal condition and a nonconvex right-hand side. Our technique is based on fixed point theorems for multivalued maps.
MSC:
34G20Nonlinear ODE in abstract spaces
47D06One-parameter semigroups and linear evolution equations
47N20Applications of operator theory to differential and integral equations
References:
[1]Byszewski, L.: Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. math. Anal. appl. 162, 494-505 (1991) · Zbl 0748.34040 · doi:10.1016/0022-247X(91)90164-U
[2]Balachandran, K.; Uchiyama, K.: Existence of solutions of nonlinear integrodifferential equations of Sobolev type with nonlocal condition in Banach spaces, Proc. indian acad. Sci. math. Sci. 110, 225-232 (2000) · Zbl 0957.34058 · doi:10.1007/BF02829493
[3]Deng, K.: Exponential decay of solutions of semilinear parabolic equations with nonlocal initial conditions, J. math. Anal. appl. 179, 630-637 (1993) · Zbl 0798.35076 · doi:10.1006/jmaa.1993.1373
[4]Boucherif, A.; Precup, R.: Semilinear evolution equations with nonlocal initial conditions, Dynam. systems appl. 16, 509-516 (2007) · Zbl 1154.34027
[5]Fu, X.; Ezzinbi, K.: Existence of solutions for neutral functional differential evolution equations with nonlocal conditions, Nonlinear anal. 54, 215-227 (2003) · Zbl 1034.34096 · doi:10.1016/S0362-546X(03)00047-6
[6]Liang, J.; Xiao, Ti-J.: Semilinear integro-differential equations with nonlocal initial conditions, Comput. math. Appl. 47, 863-875 (2004) · Zbl 1068.45014 · doi:10.1016/S0898-1221(04)90071-5
[7]Xue, X.: Existence of solutions for semilinear nonlocal Cauchy problems in Banach spaces, Electron. J. Differential equations 2005, No. 64, 1-7 (2005) · Zbl 1075.34051 · doi:emis:journals/EJDE/Volumes/2005/64/abstr.html
[8]Gatsori, E.; Ntouyas, S. K.; Sficas, Y. G.: On a nonlocal Cauchy problem for differential inclusions, Abstr. appl. Anal. 2004, No. 5, 425-434 (2004) · Zbl 1080.34005 · doi:10.1155/S108533750430610X
[9]Xue, X.; Yu, J.: Periodic solutions for semilinear evolution inclusions, J. math. Anal. appl. 331, 1246-1262 (2007) · Zbl 1125.34027 · doi:10.1016/j.jmaa.2006.09.056
[10]Zhu, L.; Li, G.: On a nonlocal problem for semilinear differential equations with upper semicontinuous nonlinearities in general Banach spaces, J. math. Anal. appl. 341, 660-675 (2008) · Zbl 1145.34034 · doi:10.1016/j.jmaa.2007.10.041
[11]A. Boucherif, Nonlocal problems for parabolic inclusions, 2008 Preprint
[12]Aubin, J. P.; Cellina, A.: Differential inclusions, (1984)
[13]Deimling, K.: Multivalued differential equations, (1992) · Zbl 0760.34002
[14]Hu, S.; Papageorgiou, N. S.: Handbook of multivalued analysis, vol. I: theory, (2000)
[15]Tolstonogov, A. A.: Differential inclusions in a Banach space, Mathematics and its applications 524 (2000) · Zbl 1021.34002
[16]Pazy, A.: Semigroups of linear operators and applications to partial differential equations, (1983)
[17]Nadler, S. B.: Multivalued contraction mappings, Pacific J. Math. 30, 475-488 (1969) · Zbl 0187.45002
[18]Bressan, A.; Colombo, G.: Extensions and selections of maps with decomposable values, Studia math. 90, 69-86 (1988) · Zbl 0677.54013
[19]O’regan, D.: Integral inclusions of upper semicontinuous or lower semicontinuous type, Proc. amer. Math. soc. 124, 2391-2399 (1996) · Zbl 0860.45007 · doi:10.1090/S0002-9939-96-03456-9
[20]Hofbauer, J.; Simon, P. L.: An existence theorem for parabolic equations on RN with discontinuous nonlinearity, Electron. J. Qual. theory differ. Equ., No. 8, 1-9 (2001) · Zbl 1056.35082 · doi:emis:journals/EJQTDE/2001/200108.html