Existence of solutions of nonlinear integrodifferential equations of Sobolev type with nonlocal condition in Banach spaces

Proceedings of the Indian Academy of Sciences: Mathematical Sciences

Volumn 110, Issue 2, 2000, Pages 225-232

  Balachandran, K ^a   Uchiyama, K ^b  

^a BHARATHIAR UNIVERSITY   (India)

^b SOPHIA UNIVERSITY   (Japan)

Author keywords

Integrodifferential equation; Nonlocal condition; Schauder's fixed point theorem; Sobolev type; Uniformly continuous semigroup

Indexed keywords

EID: 0043190843     PISSN: 02534142     EISSN: None     Source Type: Journal    
DOI: 10.1007/BF02829493     Document Type: Article

References (17)

1. Balachandran K and Chandrasekaran M, Existence of solutions of nonlinear integrodifferential equations with nonlocal condition, J. Appl. Math. Stoch. Anal. 10 (1997) 279-288
2. Balachandran K and Chandrasekaran M, Existence of solutions of a delay differential equation with nonlocal condition, Indian J. Pure. Appl. Math. 27 (1996) 443-449
3. Balachandran K, Park D G and Kwun Y C, Nonlinear integrodifferential equations of Sobolev type with nonlocal conditions in Banach spaces, Comm. Korean Math. Soc. 14 (1999) 223-231
4. Balachandran K and Ilamaran S, Existence and uniqueness of mild and strong solutions of a Volterra integrodifferential equation with nonlocal conditions, Tamkang J. Math. 28 (1997) 93-100
5. Barenblatt G, Zheltov I and Kochina I, Basic concepts in the theory of seepage of homogeneous liquids in fissured rocks, J. Appl. Math. Mech. 24 (1960) 1286-1303
6. Brill H, A semilinear Sobolev evolution equation in Banach space, J. Diff. Eq. 24 (1977) 412-425
7. Byszewski L, Theorems about the existence and uniqueness of solutions of a semilinear evolution nonlocal Cauchy problem, J. Math. Anal. Appl. 162 (1991) 494-505
8. Byszewski L. Applications of properties of the right hand sides of evolution equations to an investigation of nonlocal evolution problems. Nonlinear Anal. 33 (1998) 413-426
9. Chen P J and Curtin M E, On a theory of heat conduction involving two temperatures, Z. Angew. Math. Phys. 19 (1968) 614-627
10. Huilgol R, A second order fluid of the differential type, Internat. J. Nonlinear Mech. 3 (1968) 471-482
11. Jackson D, Existence and uniqueness of solutions to semilinear nonlocal parabolic equations, J. Math. Anal. Appl. 172 (1993) 256-265
12. Lightbourne J H III and Rankin S M III, A partial functional differential equation of Sobolev type, J. Math. Anal. Appl. 93 (1983) 328-337
13. Lin Y and Liu J U, Semilinear integrodifferential equations with nonlocal Cauchy problem, Nonlinear Anal. TMA. 26 (1996) 1023-1033
14. Ntouyas S K and Tsamatos P Ch, Global existence of semilinear evolution equation with nonlocal conditions. J. Math. Anal. Appl. 210 (1997) 679-687
15. Pazy A. Semigroups of linear operators and applications to partial differential equations. (New York: Springer-Verlag) (1983)
16. Showalter R E, Existence and representation theorem for a semilinear Sobolev equation in Banach space, SIAM J. Math. Anal. 3 (1972) 527-543
17. Ting T W, Certain nonsteady flows of second order fluids. Arch. Rational Mech. Anal. 14 (1963) 1-26