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Original Articles

Existence of Solutions for Fourth Order Boundary Value Problems on a Time Scale

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Pages 15-28 | Received 14 Sep 2001, Published online: 01 Apr 2010

References

  • Agarwal , R. P. and Bohner , M. 1998 . Quadratic functionals for second order matrix equations on time scales . Nonlinear Anal. , 33 : 675 – 692 .
  • Agarwal , R. P. and Bohner , M. 1999 . Basic calculus on time scales and some of its applications . Results Math. , 35 : 3 – 22 .
  • Kaymakçalan , B. , Lakshmikantham , V. and Sivasundaram , S. 1996 . Dynamic Systems on Measure Chains Dordrecht : Kluwer Academic .
  • Hilger , S. 1990 . Ananlysis on meaure chains—a unified approach to continuous and discrete calculus . Results Math. , 18 : 18 – 56 .
  • Agarwal , R. P. , Bohner , M. and Wong , P. J. Y. 1999 . Positive solutions and eigenvalues of conjugate boundary value problems . Proc. Edinburgh Math. Soc. , 42 : 349 – 374 .
  • Akin , E. 2000 . Boundary value problems for a differential equation on a measure chain . Panamer. Math. J. , 10 : 17 – 30 .
  • Bohner , M. and Eloe , P. W. 2000 . Higher order dynamic equations: Wronskians, disconjugacy and interpolating families of functions . J. Math. Anal. Appl. , 246 : 639 – 656 .
  • Bohner , M. and Peterson , A. 2001 . Dynamic Equations on Time Scales: An Introduction with Applications Boston : Birkhäuser .
  • Chyan , C. J. and Henderson , J. 2000 . Eigenvalue problems for nonlinear differential equations on a measure chain . J. Math. Anal. Appl. , 245 : 547 – 559 .
  • Chyan , C. J. , Davis , J. M. , Henderson , J. and Yin , W. K. C. 1998 . Eigenvalue comparisons for nonlinear differential equations on a measure chain . Elec. J. Differ. Eqs. , 35 : 1 – 7 .
  • Erbe , L. and Hilger , S. 1993 . Sturmian theory on measure chains . Differ. Eqs Dyn. Syst. , 1 : 223 – 244 .
  • Erbe , L. and Peterson , A. 1999 . Green's functions and comparison theorems for differential equations on measure chains . Dyn. Contin. Discrete Impuls. Syst. , 6 : 121 – 137 .
  • Erbe , L. and Peterson , A. 2000 . Eigenvalue conditions and positive solutions . J. Differ. Eqs Appl. , 6 : 165 – 191 .
  • Henderson , J. 2000 . Multiple solutions for 2mth order Sturm—Liouville boundary value problems on a measure chain . J. Differ. Eqs Appl. , 6 : 417 – 429 .
  • Henderson , J. and Prasad , K. R. 2001 . Existence and uniqueness of solutions of three-point boundary value problems on time scales by solution matching . Nonlinear Stud. , 8 : 1 – 12 .
  • Hartman , P. 1971 . On n-parameter families and interpolation problems for nonlinear ordinary differential equations . Trans. Am. Math. Soc. , 154 : 201 – 226 .
  • Klaasen , G. 1973 . Existence theorems for boundary value problems for n th order ordinary differential equations . Rocky Mt. J. Math. , 3 : 457 – 472 .
  • Henderson , J. 1989 . Existence theorems for boundary value problems for n th-order nonlinear difference equations . SIAM J. Math. Anal. , 20 : 468 – 478 .
  • Davis , J. M. and Henderson , J. 1998 . Uniqueness implies existence for fourth-order Lidstone boundary value problems . Panamer. Math. J. , 8 : 23 – 35 .
  • Henderson , J. 1989 . Focal boundary value problems for nonlinear difference equations, I . J. Math. Anal. Appl. , 141 : 559 – 567 .
  • Henderson , J. 1989 . Focal boundary value problems for nonlinear difference equations, II . J. Math. Anal. Appl. , 141 : 568 – 579 .
  • Chyan , C. J. 2001 . Uniqueness implies existence for second order differential equations on measure chains . J. Math. Anal. Appl. , 258 : 359 – 365 .
  • Agarwal , R. P. 1997 . “ Compactness condition for boundary value problems ” . In Equadiff9 Proc. Brno
  • Schrader , K. 1985 . Uniqueness implies existence for solutions of nonlinear boundary value problems . Abstr. Am. Math. Soc. , 6 : 235
  • Chyan , C. J. and Yin , W. K.C. A converegence theorem on a measure chain, preprint
  • Jackson , L. K. 1973 . Uniqueness of solutions of boundary value problems for ordinary differential equations . SIAM J. Appl. Math. , 24 : 535 – 538 .
  • Henderson , J. 1981 . Uniqueness of solutions of right focal boundary value problems for ordinary differential equations . J. Differ. Eqs , 41 : 218 – 227 .
  • Henderson , J. and Yin , W. 2002 . “ Existence of solutions for third order boundary value problems on a time scale ” . In Comp. Math. Appl. In press

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