Boundary value problem for second-order differential operators with nonregular integral boundary conditions

Rocky Mountain Journal of Mathematics

Volumn 36, Issue 3, 2006, Pages 893-913

  Denche, M ^a   Kourta, A ^a  

^a Universite Mentouri Constantine   (Algeria)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 33749572998     PISSN: 00357596     EISSN: None     Source Type: Journal    
DOI: 10.1216/rmjm/1181069435     Document Type: Article

References (38)

1. S.A. Beilin, Existence of solutions for one-dimensional wave equations with nonlocal conditions, Electron. J. Differential Equations 2001 (2001), 1-8.
2. H.E. Benzinger, Green's function for ordinary differential operators, J. Differ. Equ. 7 (1970), 478-496 (transl. of Differ. Uravn.).
3. J.R. Cannon, Y. Lin and J. Van Der Hook, A quasi-linear parabolic equation with nonlocal boundary conditions, Rend. Mat. Appl. (7) 9 (1989), 239-264.
4. M. Denche, Defect-coerciveness for non regular transmission problem, Adv. Math. Sci. Appl. 9(1999), 229-241.
5. M. Denche and A.L. Marhoune, Mixed problem with nonlocal boundary conditions for a third-order partial differential equation of mixed type, Internat. J. Math. Math. Sci. 26 (2001), 417-426.
6. _, Mixed problem with integral boundary condition for a high order mixed type partial differential equation, J. Appl. Math. Stoch. Anal. 16 (2003), 69-79.
7. N. Dunford and J.T. Schwartz, Linear operators, Part III, Spectral operators, Interscience, New York, 1971.
8. W. Eberhard and G. Freiling, Ston reguläre Eigenwert problem, Math. Z. 160 (1978), 139-161.
9. J. Farjas, J.I. Rosell, R. Herrero, R. Pons, F. Pi and G. Orriols, Equivalent low-order model for a nonlinear diffusion equation, Phys. D. 95 (1996), 107-127.
10. E.I. Galakhov and A.L. Skubachevskii, A nonlocal spectral problem, Differ. Equ. 33 (1997), 24-31 (transl. of Differ. Uravn.).
11. J.M. Gallardo, Generation of analytic semi-groups by second-order differential operators with nonseparated boundary conditions, Rocky Mountain J. Math. 30 (2000), 869-899.
12. _, Second-order differential operators with integral boundary conditions and generation of analytic semigroups, Rocky Mountain J. Math. 30 (2000), 1265-1291.
13. M.G. Gasumov and A.M. Magerramov, On fold-completeness of a system of eigenfunctions and associated functions of a class of differential operators, Akad. Nauk Azerbaǐdzhan SSR Dokl. 30 (1974), 9-12.
14. _, Investigation of a class of differential operator pencils of even order, Dokl. Akad. Nauk SSSR, 265 (1982), 277-280.
15. N.I. Ionkin, Solution of boundary value problem in heat conduction theory with nonlocal boundary conditions, Differ. Uravn. 13 (1977), 294-304.
16. _, Stability of a problem in heat conduction theory with nonlocal boundary conditions, Differ. Uravn. 15 (1979), 1279-1283.
17. N.I. Ionkin and E.I. Moiseev, A problem for the heat conduction equation with two-point boundary condition, Differ. Uravn. 15 (1979), 1284-1295.
18. N.I. Kamynin, A boundary value problem in the theory of heat conduction with non classical boundary condition, Teoret. Vychisl. Mat. Fiz. 4 (1964), 1006-1024.
19. A.P. Khromov, Eigenfunction expansions of ordinary linear differential operators in a finite interval, Soviet Math. Dokl. 3 (1962), 1510-1514.
20. Yu.A. Mamedov, On functions expansion to the series of solutions residue of irregular boundary value problems, in Investigations on differential equations, AGU named after S.M. Kirov (1984), 94-98.
21. M.A. Naimark, Linear differential operators, vols. 1 and 2, Ungar Publishing, New York, 1967.
22. M.L. Rasulov, Methods of contour integration, North-Holland, Amsterdam, 1967.
23. _, Applications of the contour integral method, Nauka, Moscow, 1975.
24. J.I. Rosell, J. Farjas, R. Herrero, F. Pi and G. Orriols, Homoclinic phenomena in opto-thermal bistability with localized absorption, Phys. D 85 (1995), 509-547.
25. A.A. Samarskii, Some problems in differential equations theory, Differ. Uravn. 16 (1980), 1925-1935.
26. A.A. Shkalikov, On completenes of eigenfunctions and associated function of an ordinary differential operator with separated irregular boundary conditions, Funktsional. Anal. i Prilozhen. 10 (1976), 69-80.
27. J.T. Silchenko, Differential equations with non-densely defined operator coefficients, generating semigroups with singularities, Nonlinear Anal. 36 (1999), 3, Ser. A: Theory Methods, 345-352.
28. Yu.T. Silchenko, An ordinary differential operator with irregular boundary conditions, Sibirsk. Mat. Zh. 40 (1999), 183-190 (in Russian);
29. Yu.T. Silchenko, Siberian Math. J. 40 (1999), 158-164 (in English).
30. 2 (0, 1), Dokl. Akad. Nauk SSSR 321 (1991), 1158-1163.
31. J.D. Tamarkin, About certain general problems of theory of ordinary linear differential equations and about expansions of derivative functions into series, Petrograd, 1917.
32. C. Tretter, On λ-nonlinear boundary eigenvalue problems, Akademie Verlag, Berlin, 1993.
33. A.I. Vagabov, On eigenvectors of irregular differential pencils with non-separated boundary conditions, Dokl. Akad. Nauk SSSR 261 (1981), 268-271.
34. S. Yakubov, Completness of root functions of regular differential operators, Longman Sci. & Tech., New York, 1994.
35. _, On a new method for solving irregular problems, J. Math. Anal. Appl. 220 (1998), 224-249.
36. S. Yakubov and Y. Yakubov, Differential-operator equations. Ordinary and partial differential equations, Monographs Surveys Pure Appl. Math., vol. 103, Chapman & Hall/CRC, Boca Raton, Florida, 2000.
37. Y. Yakubov, Irregular boundary value problems for ordinary differential equations, Analysis (Munich) 18 (1998), 359-402.
38. N.I. Yurchuk, Mixed problem with an integral condition for certain parabolic equations, Differ. Uravn. 22 (1986), 2117-2126.