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Volumn 69, Issue 4, 2008, Pages 1376-1388

Existence of weak solutions of two-point boundary value problems for second-order dynamic equations on time scales

Author keywords

34B10; 39A12; Boundary value problem; Critical point theory; Second order dynamic equation; Time scale

Indexed keywords

BOUNDARY CONDITIONS; BOUNDARY VALUE PROBLEMS; DIFFERENCE EQUATIONS; DIFFERENTIAL EQUATIONS; DIFFERENTIATION (CALCULUS); DYNAMIC PROGRAMMING; DYNAMICAL SYSTEMS; EQUATIONS OF STATE; INITIAL VALUE PROBLEMS; MATHEMATICAL MORPHOLOGY; MATHEMATICAL TRANSFORMATIONS; MECHANICS; NUMERICAL METHODS; ORDINARY DIFFERENTIAL EQUATIONS; SCALES (WEIGHING INSTRUMENTS);

EID: 44649201474     PISSN: 0362546X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.na.2007.06.034     Document Type: Article
Times cited : (16)

References (32)
  • 3
    • 12844263267 scopus 로고    scopus 로고
    • to V. Lakshmikantham on his 80th Birthday, Kluwer Academic Publishers, Dordrecht
    • Agarwal R.P., Bohner M., and Řehák P. to V. Lakshmikantham on his 80th Birthday. Half-Linear Dynamic Equations. Nonlinear Analysis and Applications vol. 1 (2003), Kluwer Academic Publishers, Dordrecht 1-57
    • (2003) Nonlinear Analysis and Applications , vol.1 , pp. 1-57
    • Agarwal, R.P.1    Bohner, M.2    Řehák, P.3
  • 4
    • 0000990742 scopus 로고    scopus 로고
    • Sturm-Liouville eigenvalue problems on time scales
    • Agarwal R.P., Bohner M., and Wong P.J.Y. Sturm-Liouville eigenvalue problems on time scales. Appl. Math. Comput. 99 (1999) 153-166
    • (1999) Appl. Math. Comput. , vol.99 , pp. 153-166
    • Agarwal, R.P.1    Bohner, M.2    Wong, P.J.Y.3
  • 5
    • 3042601426 scopus 로고    scopus 로고
    • Multiple positive solutions of singular and nonsingular discrete problems via variational methods
    • Agarwal R.P., Perera K., and O'Regan D. Multiple positive solutions of singular and nonsingular discrete problems via variational methods. Nonlinear Anal. 58 (2004) 69-73
    • (2004) Nonlinear Anal. , vol.58 , pp. 69-73
    • Agarwal, R.P.1    Perera, K.2    O'Regan, D.3
  • 6
    • 1542406463 scopus 로고    scopus 로고
    • An even-order three-point boundary value problem on time scales
    • Anderson D.R., and Avery R.I. An even-order three-point boundary value problem on time scales. J. Math. Anal. Appl. 291 (2004) 514-525
    • (2004) J. Math. Anal. Appl. , vol.291 , pp. 514-525
    • Anderson, D.R.1    Avery, R.I.2
  • 7
    • 1842554978 scopus 로고    scopus 로고
    • First order dynamic inclusions on time scales
    • Atici F.M., and Biles D.C. First order dynamic inclusions on time scales. J. Math. Anal. Appl. 292 (2004) 222-237
    • (2004) J. Math. Anal. Appl. , vol.292 , pp. 222-237
    • Atici, F.M.1    Biles, D.C.2
  • 8
    • 0036538017 scopus 로고    scopus 로고
    • On Green's functions and positive solutions for boundary value problems on time scales
    • Atici F.M., and Guseinov G.S. On Green's functions and positive solutions for boundary value problems on time scales. J. Comput. Appl. Math. 141 (2002) 75-99
    • (2002) J. Comput. Appl. Math. , vol.141 , pp. 75-99
    • Atici, F.M.1    Guseinov, G.S.2
  • 9
    • 0242287898 scopus 로고    scopus 로고
    • Positive semidefiniteness of discrete quadratic functionals
    • Bohner M., Doslý O., and Kratz W. Positive semidefiniteness of discrete quadratic functionals. Proc. Edinb. Math. Soc. (2) 46 (2003) 627-636
    • (2003) Proc. Edinb. Math. Soc. (2) , vol.46 , pp. 627-636
    • Bohner, M.1    Doslý, O.2    Kratz, W.3
  • 10
    • 34548255891 scopus 로고    scopus 로고
    • An eigenvalue problem for linear Hamiltonian dynamic systems
    • Bohner M., and Hilscher R. An eigenvalue problem for linear Hamiltonian dynamic systems. Fasc. Math. 35 (2005) 35-49
    • (2005) Fasc. Math. , vol.35 , pp. 35-49
    • Bohner, M.1    Hilscher, R.2
  • 11
    • 0002025829 scopus 로고    scopus 로고
    • Asymptotic behavior of dynamic equations on time scales
    • Bohner M., and Lutz D.A. Asymptotic behavior of dynamic equations on time scales. J. Difference Equ. Appl. 7 (2001) 21-50
    • (2001) J. Difference Equ. Appl. , vol.7 , pp. 21-50
    • Bohner, M.1    Lutz, D.A.2
  • 14
    • 1242299763 scopus 로고    scopus 로고
    • Extremal solutions and Green's functions of higher order periodic boundary value problems in time scales
    • Cabada A. Extremal solutions and Green's functions of higher order periodic boundary value problems in time scales. J. Math. Anal. Appl. 290 (2004) 35-54
    • (2004) J. Math. Anal. Appl. , vol.290 , pp. 35-54
    • Cabada, A.1
  • 15
  • 16
    • 0036537638 scopus 로고    scopus 로고
    • A necessary and sufficient condition for oscillation of the Sturm-Liouville dynamic equation on time scales
    • Doslý O., and Hilger S. A necessary and sufficient condition for oscillation of the Sturm-Liouville dynamic equation on time scales. J. Comput. Appl. Math. 141 (2002) 147-158
    • (2002) J. Comput. Appl. Math. , vol.141 , pp. 147-158
    • Doslý, O.1    Hilger, S.2
  • 17
    • 0003742471 scopus 로고    scopus 로고
    • Shandong Sci. and Tec. Press, Jinan (in Chinese)
    • Guo D.J. Nonlinear Functional Analysis (2001), Shandong Sci. and Tec. Press, Jinan (in Chinese)
    • (2001) Nonlinear Functional Analysis
    • Guo, D.J.1
  • 18
    • 7544222521 scopus 로고    scopus 로고
    • Existence of periodic solutions and subharmonic solutions on second order superlinear difference equations
    • Guo Z.M., and Yu J.S. Existence of periodic solutions and subharmonic solutions on second order superlinear difference equations. Sci. China Ser. A 33 (2003) 226-235
    • (2003) Sci. China Ser. A , vol.33 , pp. 226-235
    • Guo, Z.M.1    Yu, J.S.2
  • 19
    • 0141977370 scopus 로고    scopus 로고
    • The existence of periodic and subharmonic solutions to subquadratic second-order difference equations
    • Guo Z.M., and Yu J.S. The existence of periodic and subharmonic solutions to subquadratic second-order difference equations. J. London Math. Soc. 68 2 (2003) 419-430
    • (2003) J. London Math. Soc. , vol.68 , Issue.2 , pp. 419-430
    • Guo, Z.M.1    Yu, J.S.2
  • 20
    • 3242742992 scopus 로고    scopus 로고
    • Existence of two solutions of m-point boundary value problem for second order dynamic equations on time scales
    • He Z. Existence of two solutions of m-point boundary value problem for second order dynamic equations on time scales. J. Math. Anal. Appl. 296 (2004) 97-109
    • (2004) J. Math. Anal. Appl. , vol.296 , pp. 97-109
    • He, Z.1
  • 21
    • 84951604495 scopus 로고
    • Analysis on measure chains - A unified approach to continuous and discrete calculus
    • Hilger S. Analysis on measure chains - A unified approach to continuous and discrete calculus. Results Math. 18 (1990) 18-56
    • (1990) Results Math. , vol.18 , pp. 18-56
    • Hilger, S.1
  • 22
    • 0001028781 scopus 로고    scopus 로고
    • Differential and difference calculus - unified!
    • Hilger S. Differential and difference calculus - unified!. Nonlinear Anal. 30 (1997) 2683-2694
    • (1997) Nonlinear Anal. , vol.30 , pp. 2683-2694
    • Hilger, S.1
  • 23
    • 0000226297 scopus 로고    scopus 로고
    • Reid roundabout theorem for symplectic dynamic systems on time scales
    • Hilscher R. Reid roundabout theorem for symplectic dynamic systems on time scales. Appl. Math. Optim. 43 (2001) 129-146
    • (2001) Appl. Math. Optim. , vol.43 , pp. 129-146
    • Hilscher, R.1
  • 24
    • 0032203162 scopus 로고    scopus 로고
    • Stability of moving invariant sets and uncertain dynamic systems on time scales
    • Lakshmikantham V., and Sivasundaram S. Stability of moving invariant sets and uncertain dynamic systems on time scales. Comput. Math. Appl. 36 (1998) 339-346
    • (1998) Comput. Math. Appl. , vol.36 , pp. 339-346
    • Lakshmikantham, V.1    Sivasundaram, S.2
  • 27
    • 44649191533 scopus 로고
    • Amer. Math. Soc., Providence, R.I.
    • Rabinowitz P.H. Minimax Methods in Critical Point Theory with Applications to Differential Equations. CBMS Reg. Conf. Ser. Math. vol. 65 (1986), Amer. Math. Soc., Providence, R.I.
    • (1986) CBMS Reg. Conf. Ser. Math. , vol.65
    • Rabinowitz, P.H.1
  • 28
    • 0142031029 scopus 로고    scopus 로고
    • Oscillation of nonlinear dynamic equations on time scales
    • Saker S. Oscillation of nonlinear dynamic equations on time scales. Appl. Math. Comput. 148 (2004) 81-91
    • (2004) Appl. Math. Comput. , vol.148 , pp. 81-91
    • Saker, S.1
  • 29
    • 10644261242 scopus 로고    scopus 로고
    • Second-order periodic boundary value problems on time scales
    • Topal S.G. Second-order periodic boundary value problems on time scales. Comput. Math. Appl. 48 (2004) 637-648
    • (2004) Comput. Math. Appl. , vol.48 , pp. 637-648
    • Topal, S.G.1
  • 30
    • 7544251186 scopus 로고    scopus 로고
    • n nontrivial solutions for discrete two-point boundary value problems
    • n nontrivial solutions for discrete two-point boundary value problems. Nonlinear Anal. 59 (2004) 1181-1187
    • (2004) Nonlinear Anal. , vol.59 , pp. 1181-1187
    • Zhang, G.1    Yang, Z.L.2
  • 31
    • 10044272971 scopus 로고    scopus 로고
    • Periodic solutions of higher dimensional discrete systems
    • Zhou Z., Yu J.S., and Guo Z.M. Periodic solutions of higher dimensional discrete systems. Proc. Roy. Soc. Edinburgh Sect. A 134 (2004) 1013-1022
    • (2004) Proc. Roy. Soc. Edinburgh Sect. A , vol.134 , pp. 1013-1022
    • Zhou, Z.1    Yu, J.S.2    Guo, Z.M.3
  • 32
    • 33646756968 scopus 로고    scopus 로고
    • The existence of periodic and subharmonic solutions to subquadratic discrete Hamiltonian systems
    • Zhou Z., Yu J.S., and Guo Z.M. The existence of periodic and subharmonic solutions to subquadratic discrete Hamiltonian systems. ANZIAM J. 47 (2005) 89-102
    • (2005) ANZIAM J. , vol.47 , pp. 89-102
    • Zhou, Z.1    Yu, J.S.2    Guo, Z.M.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.