Investigation of Characteristic Curve for Sturm–Liouville Problem with Nonlocal Boundary Conditions on Torus

References

• Bitsadze , A. V. and Samarskii , A. A. 1969 . On certain simple generalizations of elliptic boundary-value problems . Dokl. Akad. Nauk SSSR , 185 ( 4 ) : 739 – 740 .
   Google Scholar
• Cannon , J. R. 1963 . The solution of the heat equation subject to specification of energy . Quart. Appl. Math. , 21 ( 2 ) : 155 – 160 .
   Google Scholar
• Čiegis , R. 2005 . Economical difference schemes for the solution of a two-dimensional parabolic problem with integral condition. Differ. Equ. . 41 ( 7 ) : 1025 – 1029 . Doi:10.1007/s10625–005–0244–9
   Google Scholar
• Čiegis , R. , Štikonas , A. , Štikonienė , O. and Suboč , O. 2002 . A monotonic finite-differenceschemefor aparabolicproblem with nonlocal conditions . Dier. Equ. , 38 ( 7 ) : 1027 – 1037 . Doi:10.1023/A:1021167932414
   Web of Science ®Google Scholar
• Čiegis , R. and Tumanova , N. 2010 . Numerical solution of parabolic problems with nonlocal boundary conditions . Numer. Funct. Anal. Optim. , 31 ( 12 ) : 1318 – 1329 . Doi:10.1080/01630563.2010.526734
   Web of Science ®Google Scholar
• Čiegis , R. , Štikonien , A. , Štikonienė , O. and Suboč , O. 2001 . Stationary problems with nonlocal boundary conditions . Math. Model. Anal. , 6 ( 2 ) : 178 – 191 .
   Google Scholar
• Čiupaila , R. , Jesevičiutė , Ž. and Sapagovas , M. 2004 . On the eigenvalue problem for one-dimensionaldierential operator with nonlocalintegral condition . Nonlinear Anal., Model. Control , 9 ( 2 ) : 109 – 116 .
   Google Scholar
• Coddington , E. A. and Levinson , N. 1955 . “ Theory of Ordinary Differential Equations ” . New York, Toronto, London : McGraw Hill Book Co., Inc. .
   Google Scholar
• Dehghan , M. 2005 . Effcient techniques for the second-order parabolic equation subject to nonlocal specifications . Appl. Numer. Math. , 52 ( 1 ) : 39 – 62 . Doi:10.1016/j.apnum.2004.02.002
   Web of Science ®Google Scholar
• Dehghan , M. 2007 . The one-dimensional heat equation subject to a boundary integral specification . Chaos Solitons Fractals , 32 ( 2 ) : 661 – 675 . Doi:10.1016/j.chaos.2005.11.010
   Web of Science ®Google Scholar
• Il'in , V. A. 1976 . Necessary and suffcient properties of being a basis of a subsystem of eigenfunctions and adjoint functions for Keldysh bundle for ordinary differential operators . Dokl. Akad. Nauk SSSR , 227 ( 4 ) : 796 – 799 .
   Google Scholar
• Il'in , V. A. and Kritskov , L. V. 2003 . Properties ofspectral expansions corresponding to non-self-adjoint differential operators . J. Math. Sci.(N.Y.) , 116 ( 5 ) : 3489 – 3550 . Doi:10.1023/A:1024180807502
   Google Scholar
• Il'in , V. A. and Moiseev , E. I. 1987 . Nonlocal boundary value problem of the first kind for a Sturm–Liouville operator in its differential and finite difference aspects . Differ. Uravn. , 23 ( 7 ) : 803 – 810 .
   Web of Science ®Google Scholar
• Il'in , V. A. and Moiseev , E. I. 1987 . Nonlocal boundary value problem of the second kind for a sturm–liouville operator . Differ. Uravn. , 23 ( 8 ) : 979 – 987 .
   Web of Science ®Google Scholar
• Ionkin , N. I. 1977 . The solution of a certain boundary value problem of the theory of heat conduction with a nonclassical boundary condition . Differ. Uravn. , 13 ( 2 ) : 294 – 304 .
   Google Scholar
• Jesevičiūtė , Ž. and Sapagovas , M. 2008 . On the stability offinite-dierence schemes for parabolic equations subject to integral conditions with applications to thermoelasticity . Comput. Methods Appl. Math. , 8 ( 4 ) : 360 – 373 .
   Google Scholar
• Kamynin , L. I. 1964 . A boundary value problem in the theory of the heat conduction with nonclassical boundary condition . Zh. Vychisl. Mat. Mat. Fiz. , 4 ( 6 ) : 1006 – 1024 .
   Google Scholar
• Ntouyas , S. K. 2005 . “ Nonlocal initial and boundary value problems: a survey ” . In Handbook of Dierential Equations, volume 2 of Ordinary Differential Equations , Edited by: Cañada , A. , Dr´abek , P. and Fonda , A. 461 – 558 . North Holland : Elsevier .
   Google Scholar
• Roman , S. and Štikonas , A. 2009 . Green's functions for stationary problems with nonlocal boundary conditions . Lith. Math. J. , 49 ( 2 ) : 190 – 202 . Doi:10.1007/s10986–009–9041–0
   Web of Science ®Google Scholar
• Romanand , S. and Štikonas , A. 2010 . Third-orderlineardifferentialequation with three additional conditions and formula for Green's function . Lith. Math. J. , 50 ( 4 ) : 426 – 446 . Doi:10.1007/s10986–010–9097-x
   Google Scholar
• Roman , S. and Štikonas , A. 2011 . Green's function for discrete second-order problems with nonlocal boundary conditions . Boundary Value Problems , (Article ID 767024):1–23, 2011. Doi:10.1155/2011/767024
   Google Scholar
• Samarskiiand , A. A. and Nikolaev , E. S. 1989 . “ Numerical Methods for Grid Equations ” . Vol. 1 , Basel, Boston : Birkhauser Verlag .
   Google Scholar
• Sapagovas , M. 2008 . On the stability of a finite-difference scheme for nonlocal parabolic boundary-value problems . Lith. Math. J. , 48 ( 3 ) : 339 – 356 . Doi:10.1007/s10986–008–9017–5
   Web of Science ®Google Scholar
• Sapagovas , M. and Čiegis , R. 1987 . On some boundary problems with nonlocal conditions . Dier. Uravn. , 23 ( 7 ) : 1268 – 1274 .
   Google Scholar
• Sapagovas , M. and Štikonienė , O. 2009 . A fourth-order alternating-direction method for difference schemes with nonlocal condition . Lith. Math. J. , 49 ( 3 ) : 309 – 305 . Doi:10.1007/s10986–009–9057–5
   Google Scholar
• Skučaitė , A. , Skučaitė-Bingelė , K. , Pečiulytė , S. and Štikonas , A. 2010 . Investigation of the spectrum for the Sturm–Liouville problem with one integral boundary condition . Nonlinear Anal., Model. Control , 15 ( 4 ) : 501 – 512 .
   Web of Science ®Google Scholar
• Štikonas , A. 2007 . The Sturm–Liouville problem with a nonlocal boundary condition . Lith. Math. J. , 47 ( 3 ) : 336 – 351 . Doi:10.1007/s10986–007–0023–9
   Web of Science ®Google Scholar
• Štikonas , A. and Roman , S. 2009 . Stationary problems with two additional conditions and formulae for green's functions . Numer. Funct. Anal. Optim. , 30 ( 9 ) : 1125 – 1144 . Numer. Funct. Anal. Optim.
   Web of Science ®Google Scholar
• Štikonas , A. and Štikonienė , O. 2009 . Characteristic functions for Sturm–Liouville problems with nonlocal boundary conditions . Math. Model. Anal. , 14 ( 2 ) : 229 – 246 . Doi:10.3846/1392–6292.2009.14.229–246
   Web of Science ®Google Scholar