Method of lower and upper solutions for a third-order three-point regular boundary value problem

Martin Šenkyřík

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (1992)

  • Volume: 31, Issue: 1, page 60-70
  • ISSN: 0231-9721

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Šenkyřík, Martin. "Method of lower and upper solutions for a third-order three-point regular boundary value problem." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 31.1 (1992): 60-70. <http://eudml.org/doc/23560>.

@article{Šenkyřík1992,
author = {Šenkyřík, Martin},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {three-point problem; growth conditions; Bernstein-Nagumo type; upper and lower solutions; Arzela-Ascoli theorem; generalized Fredholm alternative theorem},
language = {eng},
number = {1},
pages = {60-70},
publisher = {Palacký University Olomouc},
title = {Method of lower and upper solutions for a third-order three-point regular boundary value problem},
url = {http://eudml.org/doc/23560},
volume = {31},
year = {1992},
}

TY - JOUR
AU - Šenkyřík, Martin
TI - Method of lower and upper solutions for a third-order three-point regular boundary value problem
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 1992
PB - Palacký University Olomouc
VL - 31
IS - 1
SP - 60
EP - 70
LA - eng
KW - three-point problem; growth conditions; Bernstein-Nagumo type; upper and lower solutions; Arzela-Ascoli theorem; generalized Fredholm alternative theorem
UR - http://eudml.org/doc/23560
ER -

References

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  1. R.P. Agarwal, On boundary value problems y'''=f(x,y,y',y''), Bull. of the Institute of Math. Sinica, 12 (1984), 153-157. (1984) MR0765109
  2. D. Barr, T. Sherman, Existence and uniqueness of solutions of three-point boundary value problems, J. Diff. Eqs.13 (1973), 197-212. (1973) Zbl0261.34014MR0333326
  3. J. Bebernes, A sub-function aproach to boundary value problems for nonlinear ordinary differential equations, Pacif. J. Math. 13 (1963), 1063-1066. (1963) 
  4. G. Carristi, A three-point boundary value problem for a third order differential equation, Boll. Unione Mat. Ital., C4, 1 (1985), 259-269. (1985) MR0805218
  5. K.M. Das, B.S. Lalli, Boundary value problems for y'' '=f(x,y,y',y''), J. Math. Anal. Appl, 81 (1981), 300-307. (1981) Zbl0465.34012MR0622819
  6. R.E. Gaines J.L. Mawhin, Coincidence Degree and Nonlinear Differential Equations, Berlin-Heidelberg-New-York, Springer-Verlag, 1977, 262 p. (1977) MR0637067
  7. C.P. Gupta, On a third-order three-point boundary value problem at resonance, Diff. Int. Equations, Vol 2, 1 (1989), 1-12. (1989) Zbl0722.34014MR0960009
  8. G.H. Hardy J.E. Littlewood, G. Polya, Inequalities, (Russian trans.), IL, Moscow, 1970. (1970) 
  9. P. Hartman, Ordinary Differential Equations, (Russian trans.), Mir, Moscow, 1970, 720 p. (1970) Zbl0214.09101MR0352574
  10. P. Hartman, On n-parameter families and interpolation problems for nonlinear ordinary differential equations, Trans. Amer. Math. Soc. 154 (1971), 201-266. (1971) Zbl0222.34017MR0301277
  11. J. Henderson, L. Jackson, Existence and uniqueness of solutions of k-point boundary value problems for ordinary differential equations, J. Diff. Eqs. 48 (1970), 373-385. (1970) MR0702426
  12. I.T. Kiguradze, On a singular problem of Cauchy-Nicoletti, Ann. Mat. Pura ed Appl., 104 (1975), 151-175. (1975) Zbl0307.34003MR0402157
  13. I.T. Kiguradze, Some Singular Boundary Value Problems for Ordinary Differential Equations, (Russian), Univ. Press Tbilisi, 1975. (1975) MR0499402
  14. I.T. Kiguradze, Boundary problems for systems of ordinary differential equations, (Russian), Itogi nauki i tech., Sovr. pr. mat., 30, Moscow 1987. (1987) 
  15. G. Klaasen, Existence theorems for boundary value problems for n-th order differential equations, Rocky Mtn. J. Math., 3 (1973), 457-472. (1973) MR0357944
  16. E. Lepina, A. Lepin, Necessary and sufficient conditions for existence of a solution of a three-point BVP for a nonlinear third-order differential equation, (Russian), Latv. Mat. Ežeg. 8 (1970), 149-154. (1970) 
  17. I. Rachůnková, On some three-point problems for third-order differential equations, Mathematica Bohemica 117 (1992), 98-110. (1992) MR1154059
  18. M. Šenkyřík, On a third-order three-point regular boundary value problem, Acta UPO, Fac.rer.nat., Mathematica XXX, 1991. (1991) MR1166427
  19. N.I. Vasiljev, J.A. Klokov, Elements of the Theory of Boundary Value Problems for Ordinary Differential Equations, (Russian), Zinatne, Riga 1978. (1978) 

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