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Multipoint problems for degenerate abstract differential equations. (English) Zbl 1199.34286
This paper is concerned with multipoint boundary value problems for degenerate differential-operator equations of arbitrary order in a Banach space valued function space. By using the obtained results, multipoint boundary value problems for degenerate quasi-elliptic partial differential equations and infinite systems of differential equations in a cylindrical domain are discussed.
MSC:
34G10Linear ODE in abstract spaces
34B10Nonlocal and multipoint boundary value problems for ODE
References:
[1]M. S. Agranovich and M. I. Vishik, Elliptic problems with a parameter and parabolic problems of general type, Uspekhi Mat. Nauk, 19 (1964), 53–159.
[2]S. Agmon and L. Nirenberg, Properties of solutions of ordinary differential equations in Banach spaces, Comm. Pure Appl. Math., 16 (1963), 121–239. · Zbl 0117.10001 · doi:10.1002/cpa.3160160204
[3]H. Amann, Operator-valued Fourier multipliers, vector-valued Besov spaces, and applications, Math. Nachr., 186 (1997), 5–56. · Zbl 0880.42007 · doi:10.1002/mana.3211860102
[4]H. Amann, Linear and Quasi-linear Equations, 1, Birkhauser (1995).
[5]J. P. Aubin, Abstract boundary-value operators and their adjoint, Rend. Sem. Padova, 43 (1970), 1–33.
[6]A. Ashyralyev, On well-posedness of the nonlocal boundary value problem for elliptic equations, Numerical Functional Analysis & Optimization, 24 (2003), 1–15. · Zbl 1055.35018 · doi:10.1081/NFA-120020240
[7]R. P. Agarwal, R. Bohner and V. B. Shakhmurov, Maximal regular boundary value problems in Banach-valued weighted spaces, Boundary Value Problems, 1 (2005), 9–42. · Zbl 1081.35129 · doi:10.1155/BVP.2005.9
[8]O. V. Besov, V. P. P. Ilin and S. M. Nikolskii, Integral Representations of Functions and Embedding Theorems (Moscow, 1975).
[9]D. L. Burkholder, A geometrical conditions that implies the existence certain singular integral of Banach space-valued functions, in: Proc. Conf. Harmonic Analysis in honor of Anton Zygmund (Chicago, 1981, Wads Worth, Belmont, 1983), pp. 270–286.
[10]J. Bourgain, Some remarks on Banach spaces in which martingale differences are unconditional, Arkiv Math., 21 (1983), 163–168. · Zbl 0533.46008 · doi:10.1007/BF02384306
[11]G. Dore and S. Yakubov, Semigroup estimates and non coercive boundary value problems, Semigroup Form, 60 (2000), 93–121. · Zbl 0973.20055 · doi:10.1007/s002330010005
[12]G. Dore and A. Venni, On the closedness of the sum of two closed operators, Math. Z., 196 (1987), 189–201. · Zbl 0615.47002 · doi:10.1007/BF01163654
[13]N. Dunford and J. T. Schwartz, Linear Operators, Part 2: Spectral Theory, Interscience (New York, 1963).
[14]R. Denk, M. Hieber and J. Prüss, R-boundedness, Fourier multipliers and problems of elliptic and parabolic type, Mem. Amer. Math. Soc., 166 (2003), n. 788.
[15]A. Fafini, Su un problema ai limit per certa equazini astratte del secondo ordine, Rend. Sem. Mat. Univ. Padova, 53 (1975), 211–230.
[16]P. Grisvard, Commutative’ de deux foncteurs d’interpolation et applications, J. Math. Pures Appl., 45 (1966), 143–290.
[17]V. I. Gorbachuk and M. L. Gorbachuk, Boundary Value Problems for Differential-operator Equations, Naukova Dumka (Kiev, 1984).
[18]D. S. Jerison and C. E. Kenig, The Dirichlet problem in non-smooth domains, Ann. Math., 113 (1981), 367–382. · Zbl 0453.35036 · doi:10.2307/2006988
[19]H. Komatsu, Fractional powers of operators, Pac. J. Math., 19 (1966), 285–346.
[20]S. G. Krein, Linear Differential Equations in Banach Space (Providence, 1971).
[21]T. Kato, Perturbation Theory for Linear Operators, Second edition, Springer-Verlag (Berlin – New York, 1976).
[22]V. A. Kondratiev and O. A. Oleinik, Boundary value problems for partial differential equations in non-smooth domains, Russian Math. Surveys, 38 (1983), 1–86. · Zbl 0548.35018 · doi:10.1070/RM1983v038n02ABEH003470
[23]P. Kree, Sur les multiplicateurs dans FL aves poids, Annales Ins. Fourier, Grenoble, 16 (1966), 2, 191–121.
[24]J. Diestel, H. Jarchow and A. Tonge, Absolutely Summing Operators, Cambridge Univ. Press (1995).
[25]J. L. Lions and J. Peetre, Sur une classe d’espaces d’interpolation, Inst. Hautes Etudes Sci. Publ. Math., 19 (1964), 5–68. · Zbl 0148.11403 · doi:10.1007/BF02684796
[26]J. L. Lions and E. Magenes, Problems and limites non homogenes, J. d’Analyse Math., 11 (1963), 165–188. · Zbl 0117.06904 · doi:10.1007/BF02789983
[27]P. I. Lizorkin, (L p,L q)-multiplicators of Fourier integrals, Dokl. Akad. Nauk SSSR, 152 (1963), 808–811.
[28]D. Lamberton, Equations d’evalution lineaires associeees a’des semigroupes de contractions dans less espaces L p, J. Fund. Anal., 72 (1987), 252–262. · Zbl 0621.47039 · doi:10.1016/0022-1236(87)90088-7
[29]R. McConnell Terry, On Fourier multiplier transformations of Banach-valued functions, Trans. Amer. Mat. Soc., 285 (1984), 739–757. · doi:10.1090/S0002-9947-1984-0752501-X
[30]S. A. Nazarov and B. A. Plammenevskii, Elliptic Problems in Domains with Piecewise Smooth Boundaries, Walter de Gruyter (New York, 1994).
[31]G. Pisier, Les inegalites de Khintchine-Kahane d’apres C. Borel, Seminare sur la geometrie des espaces de Banach, 7 (1977–78), Ecole Polytechnique, Paris.
[32]V. P. Orlov, Regular degenerate differential operators of arbitrary order with unbounded operators coefficients, Proseeding Voronej State University, 2 (1974), 33–41.
[33]P. E. Sobolevskii, Inequalities coerciveness for abstract parabolic equations, Dokl. Akad. Nauk. SSSR, 57 (1964), 27–40.
[34]A. Ya. Shklyar, Complete second order linear differential equations in Hilbert spaces, Birkhäuser Verlag (Basel, 1997).
[35]V. B. Shakhmurov, Theorems on compactness of embedding in weighted anisotropic spaces, and their applications, Dokl. Akad. Nauk SSSR, 291 (1986), 612–616.
[36]V. B. Shakhmurov, Imbedding theorems and their applications to degenerate equations, Differential Equations, 24 (1988), 475–482.
[37]V. B. Shakhmurov, Coercive boundary value problems for regular degenerate differential-operator equations, J. Math. Anal. Appl., 292 (2004), 605–620. · Zbl 1060.35045 · doi:10.1016/j.jmaa.2003.12.032
[38]V. B. Shakhmurov, Embedding theorems and maximal regular differential operator equations in Banach-valued function spaces, J. Inequalities and Applications, 2 (2005), 329–345. · Zbl 1119.46034 · doi:10.1155/JIA.2005.329
[39]V. B. Shakhmurov, Embedding and maximal regular differential operators in Banach-valued weighted spaces, Acta Math. Sinica, 22 (2006), 1493–1508. · Zbl 1151.35020 · doi:10.1007/s10114-005-0764-5
[40]V. B. Shakhmurov, Embedding theorems in abstract function spaces and applications, Math. Sb., 134(176) (1987), 260–273.
[41]H. Triebel, Interpolation Theory. Function Spaces. Differential Operators, North-Holland (Amsterdam, 1978).
[42]L. Weis, Operator-valued Fourier multiplier theorems and maximal L p regularity, Math. Ann., 319 (2001), 735–775. · Zbl 0989.47025 · doi:10.1007/PL00004457
[43]S. Yakubov, Completeness of Root Functions of Regular Differential Operators, Longman, Scientific and Technical (New York, 1994).
[44]S. Yakubov, A nonlocal boundary value problem for elliptic differential-operator equations and applications, Integr. Equ. Oper. Theory, 35 (1999), 485–506. · Zbl 0942.35061 · doi:10.1007/BF01228044
[45]S. Yakubov and Ya. Yakubov, Differential-operator Equations. Ordinary and Partial Differential Equations, Chapman and Hall /CRC (Boca Raton, 2000).