PUBLICATIONS
- On existence and uniqueness of solutions of periodic
boundary value problems for linear hyperbolic equations. Bull. Acad. Sci. of Georgia
146 (1992), N 3, 501-505.
- On the correctness of periodic boundary value problems
for linear hyperbolic equations. Bull.
Acad. Sci. of Georgia 147 (1993), N 1, 26-30.
- On a boundary value problem for quasilinear hyperbolic
systems. (Russian) Dokl.
Akad. Nauk 328 (1993), N 2, 135-138; translation
in Russ. Acad. Sci., Dokl., Math. 47 (1993), N 1, 21–25.
- Periodic boundary value problems for linear hyperbolic
equations. I (Russian) Differ.
Uravn. 29 (1993), N 2, 281-297;
translation in Differential Equations 29 (1993), N 2,
231-245.
- Periodic boundary value problems for linear hyperbolic
equations. II. (Russian) Differ.
Uravn. 29 (1993), N 4, 637-645;
translation in Differential Equations 29 (1993), N 4,
542-549.
- Some boundary value problems for systems of linear
partial differential equations of hyperbolic type. Mem. Differential Equations Mathematical
Phys. 1 (1994), 1-144.
- On solutions that are bounded and periodic in a strip
of quasilinear hyperbolic systems. (Russian) Differ. Uravn. 30 (1994), N 10,
1760-1773;
translation in Differential Equations 30 (1994), N 10,
1628-1639.
- On an analogue of Favard's theorem for linear
hyperbolic systems. (Russian) Differ.
Uravn. 31 (1995), N 5, 910-911.
- On bounded in a strip solutions of quasilinear partial
differential equations of hyperbolic type. Applicable Analysis 58 (1995), N
3-4, 199-214.
- On periodic solutions of linear hyperbolic systems.
(Russian) Differ. Uravn.
31 (1995), N 9, 1592-1593.
- On some nonlocal problems for linear hyperbolic
systems. (Russian) Doklady
Acad. Nauk 345 (1995), N 3, 300-302.
- On sufficient conditions of existence and uniqueness
of periodic in a strip solutions of nonlinear hyperbolic equations. Mem. Differential Equations Math.
Phys. 10 (1997), 119-121.
- On unique solvability of the periodic problem in the
plane for linear hyperbolic equations. Mem.
Differential Equations Math. Phys. 10 (1997), 129-131.
- On periodic in the plane solutions of second order
linear hyperbolic systems. Arch.
Math. 33 (1997), N 4, 253-272.
- On doubly periodic solutions of one class of nonlinear
hyperbolic equations. (Russian). Differ.
Uravn. 34 (1998), N 2, 238-245; translation
in Differential Equations 34 (1998), N 2, 242-249.
- On periodic solutions of nonlinear hyperbolic
equations. Differ. Uravn.
34 (1998), N 11, 1576.
- On the correctness of the Dirichlet problem in a
characteristic rectangle for fourth order linear hyperbolic equations. Georgian Math. J 6
(1999), N 5, 447-470.
- On the Dirichlet problem in a characteristic rectangle
for fourth order linear singular hyperbolic equations. Georgian Math. J 6
(1999), N 6, 537-552.
- On periodic in the plane solutions of nonlinear
hyperbolic equations. Nonlinear
Anal. 39 (2000), N 2, Ser. A: Theory Methods,
173-185.
- On bounded and time-periodic solutions of nonlinear
wave equations. J Math. Anal. Appl. 259 (2001), N 1, 253 –276.
- On oscillatory properties of solutions of higher order
linear hyperbolic equations. (with I. P.
Stavroulakis) Advances
Math. Sci. Appl. 11 (2001), N 2, 645-672.
- On existence of oscillatory solutions to higher order
linear hyperbolic equations. (with I. P.
Stavroulakis) Mem.
Differential Equations Math. Phys. 22 (2001), 147-153.
- On doubly periodic solutions of fourth order linear
hyperbolic equations. (with V. Lakshmikantham) Nonlinear Anal. Ser. A.: Theory Methods 49 (2002), N 1,
87-112.
- On the Dirichlet problem for fourth order linear
hyperbolic equations. (with V. Lakshmikantham) Nonlinear Anal. Ser. A.: Theory Methods 49
(2002), N 2, 197-219.
- On Dirichlet problem in a characteristic rectangle for
higher order linear hyperbolic equations. (with V. Lakshmikantham) Nonlinear Anal. Ser. A.: Theory
Methods 50 (2002), N 8, 1153-1178.
- On vanishing at infinity solutions of higher order
linear hyperbolic equations. (with I. P.
Stavroulakis) J Inequalities Appl. 7 (2002), N 4, 517-553.
- Oscillation criteria for a class of partial
functional-differential equations of higher order. (with T. Kusano and N. Yoshida) J. Appl. Math. Stochastic Anal. 15
(2002), N 3, 271-282.
- On well-posedness of initial-boundary
value problems for higher order linear hyperbolic equations with two
independent variables. (with T. Kusano) (Russian) Differ. Uravn. 39 (2003), N 4, 516-526.
- On ill-posed initial-boundary value problems for
higher order linear hyperbolic equations with two independent variables.
(with T. Kusano) (Russian) Differ.
Uravn. 39 (2003), N 10, 1379-1394.
- On
initial-boundary value problems for degenerate linear hyperbolic systems. Mem. Differential Equations Math. Phys. 28 (2003), 141-146.
- On initial--boundary value
problems for degenerate nonlinear hyperbolic systems. Mem. Differential
Equations Math. Phys. 31 (2004), 113-116.
- On some boundary value
problems for nonlinear degenerate hyperbolic equations of higher order. Mem.
Differential Equations Math. Phys. 31 (2004), 117-122.
- On bounded solutions of
third order nonlinear hyperbolic equations higher order. Mem.
Differen-tial Equations Math. Phys. 32 (2004), 151-153.
- On bounded and
periodic in a strip solutions of nonlinear hyperbolic systems with two
independent variables. (with T. Kusano) Comput. and Math. 49
(2005), 335-364.
- Existence and uniqueness
theorems on periodic solutions to multidimensional linear hyperbolic
equations. Mem. Differential Equations Math. Phys. 36 (2005),
142-146.
- On Lidstone boundary value
problem for higher order nonlinear hyperbolic equations with two
independent variables. Mem. Differential Equations Math. Phys. 6 (2005), 153-156.
- On
initial-boundary value problems in bounded and unbounded domains for a
class of nonlinear hyperbolic equations of the third order. (with V.
Lakshmikantham) J Math. Anal. Appl. 324 (2006), 1242-1261.
- On doubly
periodic solutions of quasilinear hyperbolic equations of the fourth
order. (with T. Smith) Proc. Confer.
Differential & Difference Equations Appl. (Melbourne, Florida),
2006, 541-553.
- On blow-up solutions of initial characteristic problem for
nonlinear hyperbolic systems with two independent variables. (with I. Kiguradze) Mem. Differential Equations Math. Phys.
38 (2006), 146-149.
- On doubly
periodic solutions of nonlinear hyperbolic equations of higher order. Georgian Math. J 14 (2007), N 3, 457-469.
- On
solvability and well-posedness of initial-boundary value problems for
higher order nonlinear hyperbolic equations. Mem. Differential
Equations Math. Phys. 42 (2007), 145-152.
- On solvability if ill posed
initial--boundary value problems for higher order nonlinear hyperbolic
equations. Mem.
Differential Equations Math. Phys. 42 (2007), 153-160.
- On
solvability of boundary value problems for higher order nonlinear
hyperbolic equations. (with I. Kiguradze)
Nonlinear Analysis 69 (2008), 1914–1933.
- On solvability and well-posedness of boundary
value problems for nonlinear hyperbolic equations of the fourth order. Georgian Math. J 15 (2008), N 3, 555-569.
- On
solvability and unique solvability of two--point singular boundary value
problems. Nonlinear Analysis 71 (2009), 789-798.
- On some
nonlocal boundary value problems for linear singular differential
equations of higher order. Mem. Differential Equations Math. Phys. 47
(2009), 169-174.
- The Vallée-Poussin Problem for Higher Order Nonlinear
Hyperbolic Equations. Computer and
Mathematics with Applications 59
(2010), 994-1002.
- Estimates for the Cauchy function of linear singular
differential equations and some applications. Differ. Uravn. 46
(2010), No. 1, 29-46; translation in Differ.
Equ. 46 (2010), No. 1,
30-47.
- On conditions for linear singular boundary value
problems to be well-posed. Differ.
Uravn. 46 (2010), No. 2,
183-190; translation in Differ. Equ.
46 (2010), No. 2, 187-194.
- Global and blow-up solutions of the characteristic
initial value problem for second order nonlinear hyperbolic equations. Mem.
Differential Equations Math. Phys. 49
(2010), 121-138.
- Optimal conditions of
solvability of nonlocal problems for second-order ordinary differential
equations. (with I.
Kiguradze) Nonlinear Analysis 74 (2011), 757-767.