Nonlocal problems with integral conditions for elliptic equations

References

• Tikhonov IV. On the solvability of a problem with a nonlocal integral condition for a differential equation in a Banach space. Differ Equ. 1998;34(6):841–844.
   Web of Science ®Google Scholar
• Tikhonov IV. Uniqueness theorems for linear non-local problems for abstract differential equations. Izv Math. 2003;67(2):333–364. doi: 10.1070/IM2003v067n02ABEH000429
   Web of Science ®Google Scholar
• Tikhonov IV. A nonlocal problem with periodic integral condition for a differential equation a Banach space. Integral Transforms Spec Funct. 2004;4(1):49–69.
   Google Scholar
• Kozhanov AI. A time-nonlocal boundary value problem for linear parabolic equations. Sib Zh Ind Mat. 2004;7(1(17)):51–60.
   Google Scholar
• Sil'chenko Yu.T. Parabolic-type equations with nonlocal conditions. Contemp Math Fundam Trends. 2006;17:5–10.
   Google Scholar
• Kozhanov AI, Safiullova RR. Linear inverse problems for parabolic and hyperbolic equations. J Inverse Ill-Posed Probl. 2010;18(1):1–24. doi: 10.1515/jiip.2010.001
   Web of Science ®Google Scholar
• Fedorov VE, Ivanova ND, Fedorova Yu.Yu.. On a time nonlocal problem for inhomogeneous evolution equations. Sib Math J. 2014;55(4):882–897. doi: 10.1134/S0037446614040144
   Web of Science ®Google Scholar
• Kozhanov AI. Solvability of boundary value problems for linear parabolic equations with an integral condition in a time variable. Math Notes SVFU. 2014;21(4):17–25.
   Google Scholar
• Ashyralyev A, Agges N. Nonlocal boundary value hyperbolic problems involving integral conditions. Bound Value Probl. 2014;2014(1):205. doi: 10.1186/s13661-014-0205-4
   Google Scholar
• Kozhanov AI, Lukina GA. Nonlocal problems with an integral boundary condition for the differential equations of odd order. Sib Electron Math Rep. 2016;13:452–466.
   Web of Science ®Google Scholar
• Bitsadze AV, Samarskii AA. On some simplest generalizations of linear elliptic problems. Dokl Akad Nauk SSSR. 1969;185(4):739–740.
   Google Scholar
• Bitsadze AV. To the theory of nonlocal boundary value problems. Dokl Akad Nauk SSSR. 1984;277(1):17–19.
   Google Scholar
• Il'in VA, Moiseev EI. An a priori estimate for the solution of a problem associated with a nonlocal boundary value problem of the first kind. Differ Equ. 1988;24(5):519–526.
   Google Scholar
• Il'in VA, Moiseev EI. 2-D nonlocal boundary value problem for Poisson's operator in differential and difference variants. Matem Mod. 1990;2(8):139–156.
   Google Scholar
• Zhura NA. Boundary value problems of Bitsadze–Samarskii type for systems that are elliptic in the Douglas–Nirenberg sense. Differ Equ. 1992;28(1):79–88.
   Web of Science ®Google Scholar
• Gushchin AK, Mikhailov VP. On solvability of nonlocal problems for a second-order elliptic equation. Sb Math. 1995;81(1):101–136. doi: 10.1070/SM1995v081n01ABEH003617
   Web of Science ®Google Scholar
• Skubachevskii AL. Elliptic functional differential equations and applications. Operator theory. Advances and application, Vol. 91. Basel: Birkhauser; 1997.
   Google Scholar
• Gushchin AK. A condition for the compactness of operators in a certain class and its application to the analysis of the solubility of non-local problems for elliptic equations. Sb Math. 2002;193(5):649–668. doi: 10.1070/SM2002v193n05ABEH000649
   Web of Science ®Google Scholar
• Ashyraliev A. On well-posedness of the nonlocal boundary value problem for elliptic equations. Numer Funct Anal Optim. 2003;24(1–2):1–15. doi: 10.1081/NFA-120020240
   Web of Science ®Google Scholar
• Berikelashvili G. On a nonlocal boundary-value problem for two-dimensional elliptic equation. Comput Methods Appl Math. 2003;3(1):35–44.
   Google Scholar
• Ashyralyev A, Akay N. A note on the well-posedness of the nonlocal boundary value problem for elliptic difference equations. Appl Math Comput. 2006;175(1):49–60.
   Web of Science ®Google Scholar
• Skubachevskii AL. Nonclassical boundary-value problems. I. Contemp Math Fundam Trends. 2007;26:3–132.
   Google Scholar
• Ashyralyev A. A note on the Bitsadze–Samarskii type nonlocal boundary value problem in a Banach space. Math Anal Appl. 2008;344:557–573. doi: 10.1016/j.jmaa.2008.03.008
   Web of Science ®Google Scholar
• Kozhanov AI. On the solvability of spatially nonlocal problems with conditions of integral form for some classes of nonstationary equations. Differ Equ. 2015;51(8):1043–1050. doi: 10.1134/S001226611508008X
   Web of Science ®Google Scholar
• Berezanskii Yu.M. Expansions in eigenfunctions of selfadjoint operators. Providence (RI): American Mathematical Society; 1968.
   Google Scholar
• Ladyzhenskaya OA, Uraltseva NN. Linear and quasilinear elliptic equations. New York (NY): Academic Press; 1968.
   Google Scholar
• Evans LC. Partial differential equations. Novosibirsk: T. Rozhkovskaya; 2003.
   Google Scholar
• Ionkin NI. The solution of a certain boundary value problem of the theory of heat conduction with a nonclassical boundary condition. Differ Uravn. 1977;13(2):294–304.
   Google Scholar
• Samarskii AA. Some problems of the theory of differential equations. Differ Uravn. 1980;16(11):1925–1935.
   Web of Science ®Google Scholar